id	sid	tid	token	lemma	pos
american_scientific_journal-5494	1	1	210	210	NUM
american_scientific_journal-5494	1	2	american	american	ADJ
american_scientific_journal-5494	1	3	scientific	scientific	ADJ
american_scientific_journal-5494	1	4	research	research	NOUN
american_scientific_journal-5494	1	5	journal	journal	NOUN
american_scientific_journal-5494	1	6	for	for	ADP
american_scientific_journal-5494	1	7	engineering	engineering	NOUN
american_scientific_journal-5494	1	8	,	,	PUNCT
american_scientific_journal-5494	1	9	technology	technology	NOUN
american_scientific_journal-5494	1	10	,	,	PUNCT
american_scientific_journal-5494	1	11	and	and	CCONJ
american_scientific_journal-5494	1	12	sciences	science	NOUN
american_scientific_journal-5494	1	13	(	(	PUNCT
american_scientific_journal-5494	1	14	asrjets	asrjet	NOUN
american_scientific_journal-5494	1	15	)	)	PUNCT
american_scientific_journal-5494	1	16	issn	issn	PROPN
american_scientific_journal-5494	1	17	(	(	PUNCT
american_scientific_journal-5494	1	18	print	print	NOUN
american_scientific_journal-5494	1	19	)	)	PUNCT
american_scientific_journal-5494	1	20	2313	2313	NUM
american_scientific_journal-5494	1	21	-	-	SYM
american_scientific_journal-5494	1	22	4410	4410	NUM
american_scientific_journal-5494	1	23	,	,	PUNCT
american_scientific_journal-5494	1	24	issn	issn	PROPN
american_scientific_journal-5494	1	25	(	(	PUNCT
american_scientific_journal-5494	1	26	online	online	ADJ
american_scientific_journal-5494	1	27	)	)	PUNCT
american_scientific_journal-5494	1	28	2313	2313	NUM
american_scientific_journal-5494	1	29	-	-	SYM
american_scientific_journal-5494	1	30	4402	4402	NUM
american_scientific_journal-5494	1	31	©	©	PROPN
american_scientific_journal-5494	1	32	global	global	ADJ
american_scientific_journal-5494	1	33	society	society	NOUN
american_scientific_journal-5494	1	34	of	of	ADP
american_scientific_journal-5494	1	35	scientific	scientific	ADJ
american_scientific_journal-5494	1	36	research	research	NOUN
american_scientific_journal-5494	1	37	and	and	CCONJ
american_scientific_journal-5494	1	38	researchers	researcher	NOUN
american_scientific_journal-5494	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-5494	1	40	n	n	CCONJ
american_scientific_journal-5494	1	41	-	-	PUNCT
american_scientific_journal-5494	1	42	dimensional	dimensional	ADJ
american_scientific_journal-5494	1	43	fractional	fractional	ADJ
american_scientific_journal-5494	1	44	fourier	fourier	NOUN
american_scientific_journal-5494	1	45	transform	transform	NOUN
american_scientific_journal-5494	1	46	and	and	CCONJ
american_scientific_journal-5494	1	47	its	its	PRON
american_scientific_journal-5494	1	48	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	1	49	and	and	CCONJ
american_scientific_journal-5494	1	50	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	1	51	inayat	inayat	PROPN
american_scientific_journal-5494	1	52	ullah	ullah	PROPN
american_scientific_journal-5494	1	53	a	a	PRON
american_scientific_journal-5494	1	54	,	,	PUNCT
american_scientific_journal-5494	1	55	saleem	saleem	PROPN
american_scientific_journal-5494	1	56	iqbal	iqbal	PROPN
american_scientific_journal-5494	1	57	b	b	PROPN
american_scientific_journal-5494	1	58	*	*	PROPN
american_scientific_journal-5494	1	59	,	,	PUNCT
american_scientific_journal-5494	1	60	farhana	farhana	PROPN
american_scientific_journal-5494	1	61	sarwar	sarwar	PROPN
american_scientific_journal-5494	1	62	c	c	PROPN
american_scientific_journal-5494	1	63	,	,	PUNCT
american_scientific_journal-5494	1	64	abdul	abdul	PROPN
american_scientific_journal-5494	1	65	rehman	rehman	PROPN
american_scientific_journal-5494	1	66	d	d	PROPN
american_scientific_journal-5494	1	67	a	a	DET
american_scientific_journal-5494	1	68	,	,	PUNCT
american_scientific_journal-5494	1	69	b	b	NOUN
american_scientific_journal-5494	1	70	,	,	PUNCT
american_scientific_journal-5494	1	71	d	d	PROPN
american_scientific_journal-5494	1	72	department	department	NOUN
american_scientific_journal-5494	1	73	of	of	ADP
american_scientific_journal-5494	1	74	mathematics	mathematics	PROPN
american_scientific_journal-5494	1	75	,	,	PUNCT
american_scientific_journal-5494	1	76	university	university	NOUN
american_scientific_journal-5494	1	77	of	of	ADP
american_scientific_journal-5494	1	78	balochistan	balochistan	PROPN
american_scientific_journal-5494	1	79	,	,	PUNCT
american_scientific_journal-5494	1	80	quetta	quetta	PROPN
american_scientific_journal-5494	1	81	87300	87300	NUM
american_scientific_journal-5494	1	82	,	,	PUNCT
american_scientific_journal-5494	1	83	pakistan	pakistan	PROPN
american_scientific_journal-5494	1	84	c	c	PROPN
american_scientific_journal-5494	1	85	department	department	PROPN
american_scientific_journal-5494	1	86	of	of	ADP
american_scientific_journal-5494	1	87	mathematics	mathematics	PROPN
american_scientific_journal-5494	1	88	f.g.girls	f.g.girl	NOUN
american_scientific_journal-5494	1	89	degree	degree	NOUN
american_scientific_journal-5494	1	90	college	college	NOUN
american_scientific_journal-5494	1	91	,	,	PUNCT
american_scientific_journal-5494	1	92	madrissa	madrissa	NOUN
american_scientific_journal-5494	1	93	road	road	NOUN
american_scientific_journal-5494	1	94	,	,	PUNCT
american_scientific_journal-5494	1	95	quetta	quetta	PROPN
american_scientific_journal-5494	1	96	,	,	PUNCT
american_scientific_journal-5494	1	97	cantt	cantt	PROPN
american_scientific_journal-5494	1	98	,	,	PUNCT
american_scientific_journal-5494	1	99	87300	87300	NUM
american_scientific_journal-5494	1	100	,	,	PUNCT
american_scientific_journal-5494	1	101	pakistan	pakistan	PROPN
american_scientific_journal-5494	1	102	a	a	DET
american_scientific_journal-5494	1	103	email	email	NOUN
american_scientific_journal-5494	1	104	:	:	PUNCT
american_scientific_journal-5494	1	105	inayat1611@yahoo.com	inayat1611@yahoo.com	X
american_scientific_journal-5494	2	1	b	b	X
american_scientific_journal-5494	2	2	email	email	NOUN
american_scientific_journal-5494	2	3	:	:	PUNCT
american_scientific_journal-5494	2	4	saleemiqbal81@yahoo.com	saleemiqbal81@yahoo.com	X
american_scientific_journal-5494	2	5	c	c	NOUN
american_scientific_journal-5494	2	6	email	email	NOUN
american_scientific_journal-5494	2	7	:	:	PUNCT
american_scientific_journal-5494	2	8	f_saleem10@yahoo.com	f_saleem10@yahoo.com	X
american_scientific_journal-5494	3	1	d	d	X
american_scientific_journal-5494	3	2	email	email	NOUN
american_scientific_journal-5494	3	3	:	:	PUNCT
american_scientific_journal-5494	3	4	abdul_maths@yahoo.com	abdul_maths@yahoo.com	X
american_scientific_journal-5494	3	5	abstract	abstract	ADJ
american_scientific_journal-5494	3	6	in	in	ADP
american_scientific_journal-5494	3	7	this	this	DET
american_scientific_journal-5494	3	8	paper	paper	NOUN
american_scientific_journal-5494	3	9	,	,	PUNCT
american_scientific_journal-5494	3	10	we	we	PRON
american_scientific_journal-5494	3	11	have	have	AUX
american_scientific_journal-5494	3	12	established	establish	VERB
american_scientific_journal-5494	3	13	the	the	DET
american_scientific_journal-5494	3	14	ndimentional	ndimentional	ADJ
american_scientific_journal-5494	3	15	fractional	fractional	ADJ
american_scientific_journal-5494	3	16	fourier	fourier	NOUN
american_scientific_journal-5494	3	17	transform	transform	NOUN
american_scientific_journal-5494	3	18	and	and	CCONJ
american_scientific_journal-5494	3	19	its	its	PRON
american_scientific_journal-5494	3	20	mathematical	mathematical	ADJ
american_scientific_journal-5494	3	21	expression	expression	NOUN
american_scientific_journal-5494	3	22	in	in	ADP
american_scientific_journal-5494	3	23	a	a	DET
american_scientific_journal-5494	3	24	easier	easy	ADJ
american_scientific_journal-5494	3	25	manner	manner	NOUN
american_scientific_journal-5494	3	26	and	and	CCONJ
american_scientific_journal-5494	3	27	discus	discus	VERB
american_scientific_journal-5494	3	28	the	the	DET
american_scientific_journal-5494	3	29	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	3	30	and	and	CCONJ
american_scientific_journal-5494	3	31	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	3	32	of	of	ADP
american_scientific_journal-5494	3	33	-dimensional	-dimensional	ADJ
american_scientific_journal-5494	3	34	fractional	fractional	ADJ
american_scientific_journal-5494	3	35	fourier	fourier	NOUN
american_scientific_journal-5494	3	36	transform	transform	NOUN
american_scientific_journal-5494	3	37	.	.	PUNCT
american_scientific_journal-5494	4	1	keywords	keyword	NOUN
american_scientific_journal-5494	4	2	:	:	PUNCT
american_scientific_journal-5494	4	3	fourier	fourier	NOUN
american_scientific_journal-5494	4	4	transform	transform	NOUN
american_scientific_journal-5494	4	5	;	;	PUNCT
american_scientific_journal-5494	4	6	fractional	fractional	ADJ
american_scientific_journal-5494	4	7	fourier	fourier	NOUN
american_scientific_journal-5494	4	8	transform	transform	NOUN
american_scientific_journal-5494	4	9	;	;	PUNCT
american_scientific_journal-5494	4	10	eigenvalues;eigenfunctions	eigenvalues;eigenfunction	NOUN
american_scientific_journal-5494	4	11	.	.	PUNCT
american_scientific_journal-5494	5	1	1	1	X
american_scientific_journal-5494	5	2	.	.	X
american_scientific_journal-5494	5	3	introduction	introduction	NOUN
american_scientific_journal-5494	5	4	in	in	ADP
american_scientific_journal-5494	5	5	1929	1929	NUM
american_scientific_journal-5494	5	6	norbert	norbert	PROPN
american_scientific_journal-5494	5	7	wiener	wiener	NOUN
american_scientific_journal-5494	5	8	introduce	introduce	VERB
american_scientific_journal-5494	5	9	the	the	DET
american_scientific_journal-5494	5	10	idea	idea	NOUN
american_scientific_journal-5494	5	11	of	of	ADP
american_scientific_journal-5494	5	12	the	the	DET
american_scientific_journal-5494	5	13	fractional	fractional	ADJ
american_scientific_journal-5494	5	14	power	power	NOUN
american_scientific_journal-5494	5	15	of	of	ADP
american_scientific_journal-5494	5	16	the	the	DET
american_scientific_journal-5494	5	17	fourier	fourier	NOUN
american_scientific_journal-5494	5	18	operator[1	operator[1	NOUN
american_scientific_journal-5494	5	19	]	]	PUNCT
american_scientific_journal-5494	5	20	,	,	PUNCT
american_scientific_journal-5494	5	21	later	later	ADV
american_scientific_journal-5494	5	22	in	in	ADP
american_scientific_journal-5494	5	23	1	1	NUM
american_scientific_journal-5494	5	24	in	in	ADP
american_scientific_journal-5494	5	25	1937	1937	NUM
american_scientific_journal-5494	5	26	and	and	CCONJ
american_scientific_journal-5494	5	27	1939	1939	NUM
american_scientific_journal-5494	5	28	condon	condon	PROPN
american_scientific_journal-5494	5	29	and	and	CCONJ
american_scientific_journal-5494	5	30	kober	kober	PROPN
american_scientific_journal-5494	5	31	extended	extend	VERB
american_scientific_journal-5494	5	32	this	this	DET
american_scientific_journal-5494	5	33	idea	idea	NOUN
american_scientific_journal-5494	5	34	of	of	ADP
american_scientific_journal-5494	5	35	fractional	fractional	ADJ
american_scientific_journal-5494	5	36	order	order	NOUN
american_scientific_journal-5494	5	37	[	[	X
american_scientific_journal-5494	5	38	2,3	2,3	NUM
american_scientific_journal-5494	5	39	]	]	PUNCT
american_scientific_journal-5494	5	40	but	but	CCONJ
american_scientific_journal-5494	5	41	it	it	PRON
american_scientific_journal-5494	5	42	is	be	AUX
american_scientific_journal-5494	5	43	established	establish	VERB
american_scientific_journal-5494	5	44	in	in	ADP
american_scientific_journal-5494	5	45	more	more	ADV
american_scientific_journal-5494	5	46	precise	precise	ADJ
american_scientific_journal-5494	5	47	manner	manner	NOUN
american_scientific_journal-5494	5	48	by	by	ADP
american_scientific_journal-5494	5	49	victor	victor	PROPN
american_scientific_journal-5494	5	50	namias	namias	PROPN
american_scientific_journal-5494	5	51	in	in	ADP
american_scientific_journal-5494	5	52	1980	1980	NUM
american_scientific_journal-5494	5	53	and	and	CCONJ
american_scientific_journal-5494	5	54	introduced	introduce	VERB
american_scientific_journal-5494	5	55	the	the	DET
american_scientific_journal-5494	5	56	fractional	fractional	ADJ
american_scientific_journal-5494	5	57	fourier	fourier	NOUN
american_scientific_journal-5494	5	58	transform	transform	NOUN
american_scientific_journal-5494	5	59	as	as	ADP
american_scientific_journal-5494	5	60	a	a	DET
american_scientific_journal-5494	5	61	generalized	generalized	ADJ
american_scientific_journal-5494	5	62	form	form	NOUN
american_scientific_journal-5494	5	63	of	of	ADP
american_scientific_journal-5494	5	64	classical	classical	ADJ
american_scientific_journal-5494	5	65	fourier	fourier	NOUN
american_scientific_journal-5494	5	66	transform	transform	NOUN
american_scientific_journal-5494	5	67	and	and	CCONJ
american_scientific_journal-5494	5	68	successfully	successfully	ADV
american_scientific_journal-5494	5	69	established	establish	VERB
american_scientific_journal-5494	5	70	the	the	DET
american_scientific_journal-5494	5	71	mathematical	mathematical	ADJ
american_scientific_journal-5494	5	72	properties	property	NOUN
american_scientific_journal-5494	5	73	of	of	ADP
american_scientific_journal-5494	5	74	this	this	DET
american_scientific_journal-5494	5	75	very	very	ADV
american_scientific_journal-5494	5	76	important	important	ADJ
american_scientific_journal-5494	5	77	transform	transform	NOUN
american_scientific_journal-5494	5	78	,	,	PUNCT
american_scientific_journal-5494	5	79	he	he	PRON
american_scientific_journal-5494	5	80	also	also	ADV
american_scientific_journal-5494	5	81	applied	apply	VERB
american_scientific_journal-5494	5	82	the	the	DET
american_scientific_journal-5494	5	83	frft	frft	NOUN
american_scientific_journal-5494	5	84	to	to	PART
american_scientific_journal-5494	5	85	solve	solve	VERB
american_scientific_journal-5494	5	86	the	the	DET
american_scientific_journal-5494	5	87	schrodinger	schrodinger	PROPN
american_scientific_journal-5494	5	88	wave	wave	NOUN
american_scientific_journal-5494	5	89	equations	equation	NOUN
american_scientific_journal-5494	5	90	[	[	X
american_scientific_journal-5494	5	91	4	4	NUM
american_scientific_journal-5494	5	92	]	]	PUNCT
american_scientific_journal-5494	5	93	.	.	PUNCT
american_scientific_journal-5494	6	1	later	later	ADV
american_scientific_journal-5494	6	2	on	on	ADP
american_scientific_journal-5494	6	3	mcbride	mcbride	PROPN
american_scientific_journal-5494	6	4	and	and	CCONJ
american_scientific_journal-5494	6	5	kerr	kerr	PROPN
american_scientific_journal-5494	6	6	extended	extend	VERB
american_scientific_journal-5494	6	7	this	this	DET
american_scientific_journal-5494	6	8	1idea	1idea	NUM
american_scientific_journal-5494	6	9	of	of	ADP
american_scientific_journal-5494	6	10	fractional	fractional	ADJ
american_scientific_journal-5494	6	11	powers	power	NOUN
american_scientific_journal-5494	6	12	of	of	ADP
american_scientific_journal-5494	6	13	the	the	DET
american_scientific_journal-5494	6	14	fourier	fourier	NOUN
american_scientific_journal-5494	6	15	operator	operator	NOUN
american_scientific_journal-5494	6	16	in	in	ADP
american_scientific_journal-5494	6	17	terms	term	NOUN
american_scientific_journal-5494	6	18	of	of	ADP
american_scientific_journal-5494	6	19	mathematical	mathematical	ADJ
american_scientific_journal-5494	6	20	formulation	formulation	NOUN
american_scientific_journal-5494	6	21	[	[	PUNCT
american_scientific_journal-5494	6	22	5	5	NUM
american_scientific_journal-5494	6	23	]	]	PUNCT
american_scientific_journal-5494	6	24	and	and	CCONJ
american_scientific_journal-5494	6	25	in	in	ADP
american_scientific_journal-5494	6	26	1994	1994	NUM
american_scientific_journal-5494	6	27	almaida	almaida	PROPN
american_scientific_journal-5494	6	28	used	use	VERB
american_scientific_journal-5494	6	29	this	this	DET
american_scientific_journal-5494	6	30	transform	transform	NOUN
american_scientific_journal-5494	6	31	in	in	ADP
american_scientific_journal-5494	6	32	time	time	NOUN
american_scientific_journal-5494	6	33	frequency	frequency	NOUN
american_scientific_journal-5494	6	34	plane	plane	NOUN
american_scientific_journal-5494	6	35	[	[	X
american_scientific_journal-5494	6	36	6	6	NUM
american_scientific_journal-5494	6	37	]	]	PUNCT
american_scientific_journal-5494	6	38	.	.	PUNCT
american_scientific_journal-5494	7	1	frft	frft	ADJ
american_scientific_journal-5494	7	2	has	have	AUX
american_scientific_journal-5494	7	3	been	be	AUX
american_scientific_journal-5494	7	4	used	use	VERB
american_scientific_journal-5494	7	5	quantum	quantum	ADJ
american_scientific_journal-5494	7	6	mechanics	mechanic	NOUN
american_scientific_journal-5494	7	7	,	,	PUNCT
american_scientific_journal-5494	7	8	optics	optic	NOUN
american_scientific_journal-5494	7	9	and	and	CCONJ
american_scientific_journal-5494	7	10	signal	signal	ADJ
american_scientific_journal-5494	7	11	processing	processing	NOUN
american_scientific_journal-5494	7	12	.	.	PUNCT
american_scientific_journal-5494	8	1	since	since	SCONJ
american_scientific_journal-5494	8	2	1990	1990	NUM
american_scientific_journal-5494	8	3	the	the	DET
american_scientific_journal-5494	8	4	mathematician	mathematician	NOUN
american_scientific_journal-5494	8	5	,	,	PUNCT
american_scientific_journal-5494	8	6	physicist	physicist	NOUN
american_scientific_journal-5494	8	7	and	and	CCONJ
american_scientific_journal-5494	8	8	scientist	scientist	NOUN
american_scientific_journal-5494	8	9	highly	highly	ADV
american_scientific_journal-5494	8	10	attracted	attract	VERB
american_scientific_journal-5494	8	11	towards	towards	ADP
american_scientific_journal-5494	8	12	this	this	DET
american_scientific_journal-5494	8	13	famous	famous	ADJ
american_scientific_journal-5494	8	14	transforms	transform	VERB
american_scientific_journal-5494	8	15	a	a	DET
american_scientific_journal-5494	8	16	series	series	NOUN
american_scientific_journal-5494	8	17	of	of	ADP
american_scientific_journal-5494	8	18	boom	boom	NOUN
american_scientific_journal-5494	8	19	publication	publication	NOUN
american_scientific_journal-5494	8	20	was	be	AUX
american_scientific_journal-5494	8	21	published	publish	VERB
american_scientific_journal-5494	8	22	and	and	CCONJ
american_scientific_journal-5494	8	23	it	it	PRON
american_scientific_journal-5494	8	24	is	be	AUX
american_scientific_journal-5494	8	25	still	still	ADV
american_scientific_journal-5494	8	26	going	go	VERB
american_scientific_journal-5494	8	27	on	on	ADP
american_scientific_journal-5494	8	28	.	.	PUNCT
american_scientific_journal-5494	9	1	we	we	PRON
american_scientific_journal-5494	9	2	are	be	AUX
american_scientific_journal-5494	9	3	in	in	ADP
american_scientific_journal-5494	9	4	this	this	DET
american_scientific_journal-5494	9	5	article	article	NOUN
american_scientific_journal-5494	9	6	focus	focus	VERB
american_scientific_journal-5494	9	7	with	with	ADP
american_scientific_journal-5494	9	8	the	the	DET
american_scientific_journal-5494	9	9	mathematical	mathematical	ADJ
american_scientific_journal-5494	9	10	formulation	formulation	NOUN
american_scientific_journal-5494	9	11	of	of	ADP
american_scientific_journal-5494	9	12	n	n	CCONJ
american_scientific_journal-5494	9	13	-	-	PUNCT
american_scientific_journal-5494	9	14	dimensional	dimensional	ADJ
american_scientific_journal-5494	9	15	fractional	fractional	ADJ
american_scientific_journal-5494	9	16	fourier	fourier	NOUN
american_scientific_journal-5494	9	17	transform	transform	NOUN
american_scientific_journal-5494	9	18	and	and	CCONJ
american_scientific_journal-5494	9	19	investigating	investigate	VERB
american_scientific_journal-5494	9	20	their	their	PRON
american_scientific_journal-5494	9	21	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	9	22	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	9	23	in	in	ADP
american_scientific_journal-5494	9	24	a	a	DET
american_scientific_journal-5494	9	25	similar	similar	ADJ
american_scientific_journal-5494	9	26	manner	manner	NOUN
american_scientific_journal-5494	9	27	as	as	ADP
american_scientific_journal-5494	9	28	for	for	ADP
american_scientific_journal-5494	9	29	classical	classical	ADJ
american_scientific_journal-5494	9	30	fourier	fourier	NOUN
american_scientific_journal-5494	9	31	transform	transform	NOUN
american_scientific_journal-5494	9	32	.	.	PUNCT
american_scientific_journal-5494	10	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-5494	11	1	*	*	PUNCT
american_scientific_journal-5494	11	2	corresponding	correspond	VERB
american_scientific_journal-5494	11	3	author	author	NOUN
american_scientific_journal-5494	11	4	american	american	PROPN
american_scientific_journal-5494	11	5	scientific	scientific	PROPN
american_scientific_journal-5494	11	6	research	research	PROPN
american_scientific_journal-5494	11	7	journal	journal	NOUN
american_scientific_journal-5494	11	8	for	for	ADP
american_scientific_journal-5494	11	9	engineering	engineering	NOUN
american_scientific_journal-5494	11	10	,	,	PUNCT
american_scientific_journal-5494	11	11	technology	technology	NOUN
american_scientific_journal-5494	11	12	,	,	PUNCT
american_scientific_journal-5494	11	13	and	and	CCONJ
american_scientific_journal-5494	11	14	sciences	science	NOUN
american_scientific_journal-5494	11	15	(	(	PUNCT
american_scientific_journal-5494	11	16	asrjets	asrjet	NOUN
american_scientific_journal-5494	11	17	)	)	PUNCT
american_scientific_journal-5494	11	18	(	(	PUNCT
american_scientific_journal-5494	11	19	2019	2019	NUM
american_scientific_journal-5494	11	20	)	)	PUNCT
american_scientific_journal-5494	11	21	volume	volume	NOUN
american_scientific_journal-5494	11	22	62	62	NUM
american_scientific_journal-5494	11	23	,	,	PUNCT
american_scientific_journal-5494	11	24	no	no	DET
american_scientific_journal-5494	11	25	1	1	NUM
american_scientific_journal-5494	11	26	,	,	PUNCT
american_scientific_journal-5494	11	27	pp	pp	ADV
american_scientific_journal-5494	11	28	210	210	NUM
american_scientific_journal-5494	11	29	-	-	SYM
american_scientific_journal-5494	11	30	214	214	NUM
american_scientific_journal-5494	11	31	211	211	NUM
american_scientific_journal-5494	11	32	1.1	1.1	NUM
american_scientific_journal-5494	11	33	.	.	PUNCT
american_scientific_journal-5494	12	1	the	the	DET
american_scientific_journal-5494	12	2	n	n	ADV
american_scientific_journal-5494	12	3	-	-	PUNCT
american_scientific_journal-5494	12	4	dimensional	dimensional	ADJ
american_scientific_journal-5494	12	5	fourier	fourier	NOUN
american_scientific_journal-5494	12	6	transform	transform	NOUN
american_scientific_journal-5494	12	7	(	(	PUNCT
american_scientific_journal-5494	12	8	ft	ft	NOUN
american_scientific_journal-5494	12	9	)	)	PUNCT
american_scientific_journal-5494	12	10	in	in	ADP
american_scientific_journal-5494	12	11	this	this	DET
american_scientific_journal-5494	12	12	section	section	NOUN
american_scientific_journal-5494	12	13	we	we	PRON
american_scientific_journal-5494	12	14	recall	recall	VERB
american_scientific_journal-5494	12	15	definition	definition	NOUN
american_scientific_journal-5494	12	16	and	and	CCONJ
american_scientific_journal-5494	12	17	some	some	PRON
american_scientific_journal-5494	12	18	of	of	ADP
american_scientific_journal-5494	12	19	the	the	DET
american_scientific_journal-5494	12	20	properties	property	NOUN
american_scientific_journal-5494	12	21	and	and	CCONJ
american_scientific_journal-5494	12	22	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	12	23	and	and	CCONJ
american_scientific_journal-5494	12	24	eigenfunction	eigenfunction	NOUN
american_scientific_journal-5494	12	25	of	of	ADP
american_scientific_journal-5494	12	26	the	the	DET
american_scientific_journal-5494	12	27	classical	classical	ADJ
american_scientific_journal-5494	12	28	continuous	continuous	ADJ
american_scientific_journal-5494	12	29	fourier	fourier	NOUN
american_scientific_journal-5494	12	30	transform	transform	NOUN
american_scientific_journal-5494	12	31	so	so	SCONJ
american_scientific_journal-5494	12	32	that	that	SCONJ
american_scientific_journal-5494	12	33	it	it	PRON
american_scientific_journal-5494	12	34	will	will	AUX
american_scientific_journal-5494	12	35	motivate	motivate	VERB
american_scientific_journal-5494	12	36	to	to	PART
american_scientific_journal-5494	12	37	dicuss	dicuss	VERB
american_scientific_journal-5494	12	38	the	the	DET
american_scientific_journal-5494	12	39	eigen	eigen	PROPN
american_scientific_journal-5494	12	40	values	value	NOUN
american_scientific_journal-5494	12	41	for	for	ADP
american_scientific_journal-5494	12	42	n	n	CCONJ
american_scientific_journal-5494	12	43	-	-	PUNCT
american_scientific_journal-5494	12	44	dimensional	dimensional	ADJ
american_scientific_journal-5494	12	45	fractional	fractional	ADJ
american_scientific_journal-5494	12	46	fourier	fourier	NOUN
american_scientific_journal-5494	12	47	transform	transform	NOUN
american_scientific_journal-5494	12	48	.	.	PUNCT
american_scientific_journal-5494	13	1	the	the	DET
american_scientific_journal-5494	13	2	fourier	fourier	NOUN
american_scientific_journal-5494	13	3	and	and	CCONJ
american_scientific_journal-5494	13	4	its	its	PRON
american_scientific_journal-5494	13	5	inverse	inverse	NOUN
american_scientific_journal-5494	13	6	fourier	fourier	NOUN
american_scientific_journal-5494	13	7	transform	transform	NOUN
american_scientific_journal-5494	13	8	is	be	AUX
american_scientific_journal-5494	13	9	defined	define	VERB
american_scientific_journal-5494	13	10	by	by	ADP
american_scientific_journal-5494	13	11	the	the	DET
american_scientific_journal-5494	13	12	following	follow	VERB
american_scientific_journal-5494	13	13	pair	pair	NOUN
american_scientific_journal-5494	13	14	of	of	ADP
american_scientific_journal-5494	13	15	equations	equation	NOUN
american_scientific_journal-5494	13	16	(	(	PUNCT
american_scientific_journal-5494	13	17	)	)	PUNCT
american_scientific_journal-5494	13	18	√	√	NUM
american_scientific_journal-5494	13	19	∫	∫	PROPN
american_scientific_journal-5494	13	20	(	(	PUNCT
american_scientific_journal-5494	13	21	)	)	PUNCT
american_scientific_journal-5494	13	22	(	(	PUNCT
american_scientific_journal-5494	13	23	)	)	PUNCT
american_scientific_journal-5494	13	24	(	(	PUNCT
american_scientific_journal-5494	13	25	)	)	PUNCT
american_scientific_journal-5494	13	26	√	√	NUM
american_scientific_journal-5494	13	27	∫	∫	PROPN
american_scientific_journal-5494	13	28	(	(	PUNCT
american_scientific_journal-5494	13	29	)	)	PUNCT
american_scientific_journal-5494	13	30	(	(	PUNCT
american_scientific_journal-5494	13	31	)	)	PUNCT
american_scientific_journal-5494	13	32	the	the	DET
american_scientific_journal-5494	13	33	one	one	NUM
american_scientific_journal-5494	13	34	of	of	ADP
american_scientific_journal-5494	13	35	the	the	DET
american_scientific_journal-5494	13	36	main	main	ADJ
american_scientific_journal-5494	13	37	application	application	NOUN
american_scientific_journal-5494	13	38	of	of	ADP
american_scientific_journal-5494	13	39	fourier	fourier	NOUN
american_scientific_journal-5494	13	40	transform	transform	NOUN
american_scientific_journal-5494	13	41	(	(	PUNCT
american_scientific_journal-5494	13	42	ft	ft	NOUN
american_scientific_journal-5494	13	43	)	)	PUNCT
american_scientific_journal-5494	13	44	find	find	VERB
american_scientific_journal-5494	13	45	in	in	ADP
american_scientific_journal-5494	13	46	designing	designing	NOUN
american_scientific_journal-5494	13	47	of	of	ADP
american_scientific_journal-5494	13	48	filters	filter	NOUN
american_scientific_journal-5494	13	49	real	real	ADJ
american_scientific_journal-5494	13	50	filters	filter	NOUN
american_scientific_journal-5494	13	51	,	,	PUNCT
american_scientific_journal-5494	13	52	reconstruction	reconstruction	NOUN
american_scientific_journal-5494	13	53	of	of	ADP
american_scientific_journal-5494	13	54	signal	signal	NOUN
american_scientific_journal-5494	13	55	from	from	ADP
american_scientific_journal-5494	13	56	digital	digital	PROPN
american_scientific_journal-5494	13	57	to	to	AUX
american_scientific_journal-5494	13	58	analog	analog	NOUN
american_scientific_journal-5494	13	59	conversion	conversion	NOUN
american_scientific_journal-5494	13	60	,	,	PUNCT
american_scientific_journal-5494	13	61	sinusoidal	sinusoidal	ADJ
american_scientific_journal-5494	13	62	modulation	modulation	NOUN
american_scientific_journal-5494	13	63	and	and	CCONJ
american_scientific_journal-5494	13	64	pulse	pulse	NOUN
american_scientific_journal-5494	13	65	amplitude	amplitude	NOUN
american_scientific_journal-5494	13	66	modulation	modulation	NOUN
american_scientific_journal-5494	13	67	schemes	scheme	NOUN
american_scientific_journal-5494	13	68	in	in	ADP
american_scientific_journal-5494	13	69	facial	facial	ADJ
american_scientific_journal-5494	13	70	recognition	recognition	NOUN
american_scientific_journal-5494	13	71	the	the	DET
american_scientific_journal-5494	13	72	predefined	predefine	VERB
american_scientific_journal-5494	13	73	eigenfaces	eigenface	NOUN
american_scientific_journal-5494	13	74	are	be	AUX
american_scientific_journal-5494	13	75	used	use	VERB
american_scientific_journal-5494	13	76	to	to	PART
american_scientific_journal-5494	13	77	construct	construct	VERB
american_scientific_journal-5494	13	78	the	the	DET
american_scientific_journal-5494	13	79	images	image	NOUN
american_scientific_journal-5494	13	80	from	from	ADP
american_scientific_journal-5494	13	81	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	13	82	[	[	X
american_scientific_journal-5494	13	83	7	7	NUM
american_scientific_journal-5494	13	84	]	]	PUNCT
american_scientific_journal-5494	13	85	.	.	PUNCT
american_scientific_journal-5494	14	1	one	one	NUM
american_scientific_journal-5494	14	2	of	of	ADP
american_scientific_journal-5494	14	3	the	the	DET
american_scientific_journal-5494	14	4	important	important	ADJ
american_scientific_journal-5494	14	5	role	role	NOUN
american_scientific_journal-5494	14	6	of	of	ADP
american_scientific_journal-5494	14	7	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	14	8	as	as	ADP
american_scientific_journal-5494	14	9	a	a	DET
american_scientific_journal-5494	14	10	role	role	NOUN
american_scientific_journal-5494	14	11	in	in	ADP
american_scientific_journal-5494	14	12	linear	linear	ADJ
american_scientific_journal-5494	14	13	time	time	NOUN
american_scientific_journal-5494	14	14	invariant	invariant	ADJ
american_scientific_journal-5494	14	15	systems	system	NOUN
american_scientific_journal-5494	14	16	where	where	SCONJ
american_scientific_journal-5494	14	17	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	14	18	represent	represent	VERB
american_scientific_journal-5494	14	19	as	as	ADP
american_scientific_journal-5494	14	20	arbitrary	arbitrary	ADJ
american_scientific_journal-5494	14	21	signals	signal	NOUN
american_scientific_journal-5494	14	22	.the	.the	PUNCT
american_scientific_journal-5494	14	23	eigenvalues	eigenvalue	VERB
american_scientific_journal-5494	14	24	and	and	CCONJ
american_scientific_journal-5494	14	25	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	14	26	of	of	ADP
american_scientific_journal-5494	14	27	the	the	DET
american_scientific_journal-5494	14	28	ordinary	ordinary	ADJ
american_scientific_journal-5494	14	29	fourier	fourier	NOUN
american_scientific_journal-5494	14	30	transform	transform	NOUN
american_scientific_journal-5494	14	31	are	be	AUX
american_scientific_journal-5494	14	32	well	well	ADV
american_scientific_journal-5494	14	33	known	know	VERB
american_scientific_journal-5494	14	34	and	and	CCONJ
american_scientific_journal-5494	14	35	discussed	discuss	VERB
american_scientific_journal-5494	14	36	in	in	ADP
american_scientific_journal-5494	14	37	[	[	X
american_scientific_journal-5494	14	38	8	8	NUM
american_scientific_journal-5494	14	39	]	]	PUNCT
american_scientific_journal-5494	14	40	.	.	PUNCT
american_scientific_journal-5494	15	1	there	there	PRON
american_scientific_journal-5494	15	2	are	be	VERB
american_scientific_journal-5494	15	3	hermite	hermite	ADJ
american_scientific_journal-5494	15	4	-	-	PUNCT
american_scientific_journal-5494	15	5	gaussian	gaussian	ADJ
american_scientific_journal-5494	15	6	functions	function	NOUN
american_scientific_journal-5494	15	7	(	(	PUNCT
american_scientific_journal-5494	15	8	)	)	PUNCT
american_scientific_journal-5494	15	9	commonly	commonly	ADV
american_scientific_journal-5494	15	10	known	know	VERB
american_scientific_journal-5494	15	11	as	as	ADP
american_scientific_journal-5494	15	12	the	the	DET
american_scientific_journal-5494	15	13	eigensolutions	eigensolution	NOUN
american_scientific_journal-5494	15	14	of	of	ADP
american_scientific_journal-5494	15	15	the	the	DET
american_scientific_journal-5494	15	16	harmonic	harmonic	ADJ
american_scientific_journal-5494	15	17	oscillator	oscillator	NOUN
american_scientific_journal-5494	15	18	in	in	ADP
american_scientific_journal-5494	15	19	quantum	quantum	ADJ
american_scientific_journal-5494	15	20	mechanics	mechanic	NOUN
american_scientific_journal-5494	15	21	or	or	CCONJ
american_scientific_journal-5494	15	22	the	the	DET
american_scientific_journal-5494	15	23	modes	mode	NOUN
american_scientific_journal-5494	15	24	of	of	ADP
american_scientific_journal-5494	15	25	propagation	propagation	NOUN
american_scientific_journal-5494	15	26	of	of	ADP
american_scientific_journal-5494	15	27	quadratic	quadratic	ADJ
american_scientific_journal-5494	15	28	graded	grade	VERB
american_scientific_journal-5494	15	29	-	-	PUNCT
american_scientific_journal-5494	15	30	index	index	NOUN
american_scientific_journal-5494	15	31	media	medium	NOUN
american_scientific_journal-5494	15	32	in	in	ADP
american_scientific_journal-5494	15	33	optics	optic	NOUN
american_scientific_journal-5494	15	34	.	.	PUNCT
american_scientific_journal-5494	16	1	the	the	DET
american_scientific_journal-5494	16	2	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	16	3	may	may	AUX
american_scientific_journal-5494	16	4	be	be	AUX
american_scientific_journal-5494	16	5	expressed	express	VERB
american_scientific_journal-5494	16	6	as	as	ADP
american_scientific_journal-5494	16	7	(	(	PUNCT
american_scientific_journal-5494	16	8	)	)	PUNCT
american_scientific_journal-5494	16	9	and	and	CCONJ
american_scientific_journal-5494	16	10	the	the	DET
american_scientific_journal-5494	16	11	eigen	eigen	PROPN
american_scientific_journal-5494	16	12	value	value	NOUN
american_scientific_journal-5494	16	13	equation	equation	NOUN
american_scientific_journal-5494	16	14	for	for	ADP
american_scientific_journal-5494	16	15	the	the	DET
american_scientific_journal-5494	16	16	ordinary	ordinary	ADJ
american_scientific_journal-5494	16	17	fourier	fourier	NOUN
american_scientific_journal-5494	16	18	transform	transform	NOUN
american_scientific_journal-5494	16	19	may	may	AUX
american_scientific_journal-5494	16	20	be	be	AUX
american_scientific_journal-5494	16	21	written	write	VERB
american_scientific_journal-5494	16	22	as	as	ADP
american_scientific_journal-5494	16	23	(	(	PUNCT
american_scientific_journal-5494	16	24	)	)	PUNCT
american_scientific_journal-5494	16	25	(	(	PUNCT
american_scientific_journal-5494	16	26	)	)	PUNCT
american_scientific_journal-5494	16	27	(	(	PUNCT
american_scientific_journal-5494	16	28	)	)	PUNCT
american_scientific_journal-5494	16	29	a	a	DET
american_scientific_journal-5494	16	30	detailed	detailed	ADJ
american_scientific_journal-5494	16	31	discussions	discussion	NOUN
american_scientific_journal-5494	16	32	is	be	AUX
american_scientific_journal-5494	16	33	found	find	VERB
american_scientific_journal-5494	16	34	in	in	ADP
american_scientific_journal-5494	16	35	[	[	X
american_scientific_journal-5494	16	36	9	9	NUM
american_scientific_journal-5494	16	37	]	]	PUNCT
american_scientific_journal-5494	16	38	on	on	ADP
american_scientific_journal-5494	16	39	the	the	DET
american_scientific_journal-5494	16	40	analysis	analysis	NOUN
american_scientific_journal-5494	16	41	of	of	ADP
american_scientific_journal-5494	16	42	eigenvalues	eigenvalue	VERB
american_scientific_journal-5494	16	43	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	16	44	of	of	ADP
american_scientific_journal-5494	16	45	ndimensional	ndimensional	ADJ
american_scientific_journal-5494	16	46	fourier	fourier	NOUN
american_scientific_journal-5494	16	47	transform	transform	NOUN
american_scientific_journal-5494	16	48	and	and	CCONJ
american_scientific_journal-5494	16	49	are	be	AUX
american_scientific_journal-5494	16	50	given	give	VERB
american_scientific_journal-5494	16	51	by	by	ADP
american_scientific_journal-5494	16	52	(	(	PUNCT
american_scientific_journal-5494	16	53	√	√	NUM
american_scientific_journal-5494	16	54	)	)	PUNCT
american_scientific_journal-5494	16	55	(	(	PUNCT
american_scientific_journal-5494	16	56	√	√	NUM
american_scientific_journal-5494	16	57	)	)	PUNCT
american_scientific_journal-5494	16	58	(	(	PUNCT
american_scientific_journal-5494	16	59	√	√	NUM
american_scientific_journal-5494	16	60	)	)	PUNCT
american_scientific_journal-5494	16	61	(	(	PUNCT
american_scientific_journal-5494	16	62	√	√	INTJ
american_scientific_journal-5494	16	63	)	)	PUNCT
american_scientific_journal-5494	16	64	there	there	PRON
american_scientific_journal-5494	16	65	are	be	VERB
american_scientific_journal-5494	16	66	number	number	NOUN
american_scientific_journal-5494	16	67	of	of	ADP
american_scientific_journal-5494	16	68	applications	application	NOUN
american_scientific_journal-5494	16	69	of	of	ADP
american_scientific_journal-5494	16	70	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	16	71	and	and	CCONJ
american_scientific_journal-5494	16	72	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	16	73	are	be	AUX
american_scientific_journal-5494	16	74	found	find	VERB
american_scientific_journal-5494	16	75	in	in	ADP
american_scientific_journal-5494	16	76	various	various	ADJ
american_scientific_journal-5494	16	77	areas	area	NOUN
american_scientific_journal-5494	16	78	like	like	ADP
american_scientific_journal-5494	16	79	of	of	ADP
american_scientific_journal-5494	16	80	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	16	81	is	be	AUX
american_scientific_journal-5494	16	82	also	also	ADV
american_scientific_journal-5494	16	83	find	find	VERB
american_scientific_journal-5494	16	84	in	in	ADP
american_scientific_journal-5494	16	85	image	image	NOUN
american_scientific_journal-5494	16	86	processing	processing	NOUN
american_scientific_journal-5494	16	87	,	,	PUNCT
american_scientific_journal-5494	16	88	voice	voice	NOUN
american_scientific_journal-5494	16	89	recognition	recognition	NOUN
american_scientific_journal-5494	16	90	,	,	PUNCT
american_scientific_journal-5494	16	91	medical	medical	ADJ
american_scientific_journal-5494	16	92	imaging	imaging	NOUN
american_scientific_journal-5494	16	93	analysis	analysis	NOUN
american_scientific_journal-5494	16	94	,	,	PUNCT
american_scientific_journal-5494	16	95	handwriting	handwriting	NOUN
american_scientific_journal-5494	16	96	analysis	analysis	NOUN
american_scientific_journal-5494	16	97	,	,	PUNCT
american_scientific_journal-5494	16	98	lip	lip	NOUN
american_scientific_journal-5494	16	99	reading	reading	NOUN
american_scientific_journal-5494	16	100	and	and	CCONJ
american_scientific_journal-5494	16	101	sign	sign	VERB
american_scientific_journal-5494	16	102	language	language	NOUN
american_scientific_journal-5494	16	103	/	/	SYM
american_scientific_journal-5494	16	104	hand	hand	NOUN
american_scientific_journal-5494	16	105	gestures	gesture	NOUN
american_scientific_journal-5494	16	106	interpretation[9	interpretation[9	ADV
american_scientific_journal-5494	16	107	]	]	PUNCT
american_scientific_journal-5494	16	108	.	.	PUNCT
american_scientific_journal-5494	17	1	in	in	ADP
american_scientific_journal-5494	17	2	case	case	NOUN
american_scientific_journal-5494	17	3	a	a	DET
american_scientific_journal-5494	17	4	signal	signal	NOUN
american_scientific_journal-5494	17	5	is	be	AUX
american_scientific_journal-5494	17	6	represented	represent	VERB
american_scientific_journal-5494	17	7	in	in	ADP
american_scientific_journal-5494	17	8	linear	linear	ADJ
american_scientific_journal-5494	17	9	combination	combination	NOUN
american_scientific_journal-5494	17	10	of	of	ADP
american_scientific_journal-5494	17	11	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	17	12	then	then	ADV
american_scientific_journal-5494	17	13	it	it	PRON
american_scientific_journal-5494	17	14	will	will	AUX
american_scientific_journal-5494	17	15	reduce	reduce	VERB
american_scientific_journal-5494	17	16	the	the	DET
american_scientific_journal-5494	17	17	evalution	evalution	NOUN
american_scientific_journal-5494	17	18	of	of	ADP
american_scientific_journal-5494	17	19	spectrum	spectrum	NOUN
american_scientific_journal-5494	17	20	and	and	CCONJ
american_scientific_journal-5494	17	21	also	also	ADV
american_scientific_journal-5494	17	22	useful	useful	ADJ
american_scientific_journal-5494	17	23	in	in	ADP
american_scientific_journal-5494	17	24	developing	develop	VERB
american_scientific_journal-5494	17	25	.	.	PUNCT
american_scientific_journal-5494	18	1	this	this	DET
american_scientific_journal-5494	18	2	representation	representation	NOUN
american_scientific_journal-5494	18	3	is	be	AUX
american_scientific_journal-5494	18	4	also	also	ADV
american_scientific_journal-5494	18	5	useful	useful	ADJ
american_scientific_journal-5494	18	6	in	in	ADP
american_scientific_journal-5494	18	7	developing	develop	VERB
american_scientific_journal-5494	18	8	the	the	DET
american_scientific_journal-5494	18	9	new	new	ADJ
american_scientific_journal-5494	18	10	signal	signal	NOUN
american_scientific_journal-5494	18	11	compression	compression	NOUN
american_scientific_journal-5494	18	12	techniques.the	techniques.the	DET
american_scientific_journal-5494	18	13	eigenfunction	eigenfunction	NOUN
american_scientific_journal-5494	18	14	which	which	PRON
american_scientific_journal-5494	18	15	correspond	correspond	VERB
american_scientific_journal-5494	18	16	the	the	DET
american_scientific_journal-5494	18	17	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	18	18	are	be	AUX
american_scientific_journal-5494	18	19	also	also	ADV
american_scientific_journal-5494	18	20	useful	useful	ADJ
american_scientific_journal-5494	18	21	in	in	ADP
american_scientific_journal-5494	18	22	study	study	NOUN
american_scientific_journal-5494	18	23	of	of	ADP
american_scientific_journal-5494	18	24	signal	signal	ADJ
american_scientific_journal-5494	18	25	spaces	space	NOUN
american_scientific_journal-5494	18	26	spanned	span	VERB
american_scientific_journal-5494	18	27	and	and	CCONJ
american_scientific_journal-5494	18	28	can	can	AUX
american_scientific_journal-5494	18	29	revolutionize	revolutionize	VERB
american_scientific_journal-5494	18	30	the	the	DET
american_scientific_journal-5494	18	31	transmission	transmission	NOUN
american_scientific_journal-5494	18	32	of	of	ADP
american_scientific_journal-5494	18	33	data	datum	NOUN
american_scientific_journal-5494	18	34	such	such	ADJ
american_scientific_journal-5494	18	35	as	as	ADP
american_scientific_journal-5494	18	36	higher	high	ADJ
american_scientific_journal-5494	18	37	dimensional	dimensional	ADJ
american_scientific_journal-5494	18	38	signals	signal	NOUN
american_scientific_journal-5494	18	39	like	like	ADP
american_scientific_journal-5494	18	40	images	image	NOUN
american_scientific_journal-5494	18	41	,	,	PUNCT
american_scientific_journal-5494	18	42	video	video	NOUN
american_scientific_journal-5494	18	43	etc	etc	X
american_scientific_journal-5494	18	44	.	.	X
american_scientific_journal-5494	19	1	2	2	X
american_scientific_journal-5494	19	2	.	.	NOUN
american_scientific_journal-5494	19	3	results	result	NOUN
american_scientific_journal-5494	19	4	and	and	CCONJ
american_scientific_journal-5494	19	5	discussions	discussion	NOUN
american_scientific_journal-5494	19	6	2.1	2.1	NUM
american_scientific_journal-5494	19	7	.	.	PUNCT
american_scientific_journal-5494	20	1	one	one	NUM
american_scientific_journal-5494	20	2	dimensional	dimensional	ADJ
american_scientific_journal-5494	20	3	fractional	fractional	ADJ
american_scientific_journal-5494	20	4	fourier	fourier	NOUN
american_scientific_journal-5494	20	5	transform	transform	VERB
american_scientific_journal-5494	20	6	the	the	DET
american_scientific_journal-5494	20	7	one	one	NUM
american_scientific_journal-5494	20	8	dimensional	dimensional	ADJ
american_scientific_journal-5494	20	9	linear	linear	NOUN
american_scientific_journal-5494	20	10	operator	operator	NOUN
american_scientific_journal-5494	20	11	version	version	NOUN
american_scientific_journal-5494	20	12	of	of	ADP
american_scientific_journal-5494	20	13	fractional	fractional	ADJ
american_scientific_journal-5494	20	14	fourier	fourier	NOUN
american_scientific_journal-5494	20	15	transform	transform	NOUN
american_scientific_journal-5494	20	16	is	be	AUX
american_scientific_journal-5494	20	17	given	give	VERB
american_scientific_journal-5494	20	18	as	as	ADP
american_scientific_journal-5494	20	19	follows	follow	VERB
american_scientific_journal-5494	20	20	,	,	PUNCT
american_scientific_journal-5494	20	21	american	american	ADJ
american_scientific_journal-5494	20	22	scientific	scientific	ADJ
american_scientific_journal-5494	20	23	research	research	NOUN
american_scientific_journal-5494	20	24	journal	journal	NOUN
american_scientific_journal-5494	20	25	for	for	ADP
american_scientific_journal-5494	20	26	engineering	engineering	NOUN
american_scientific_journal-5494	20	27	,	,	PUNCT
american_scientific_journal-5494	20	28	technology	technology	NOUN
american_scientific_journal-5494	20	29	,	,	PUNCT
american_scientific_journal-5494	20	30	and	and	CCONJ
american_scientific_journal-5494	20	31	sciences	science	NOUN
american_scientific_journal-5494	20	32	(	(	PUNCT
american_scientific_journal-5494	20	33	asrjets	asrjet	NOUN
american_scientific_journal-5494	20	34	)	)	PUNCT
american_scientific_journal-5494	20	35	(	(	PUNCT
american_scientific_journal-5494	20	36	2019	2019	NUM
american_scientific_journal-5494	20	37	)	)	PUNCT
american_scientific_journal-5494	20	38	volume	volume	NOUN
american_scientific_journal-5494	20	39	62	62	NUM
american_scientific_journal-5494	20	40	,	,	PUNCT
american_scientific_journal-5494	20	41	no	no	DET
american_scientific_journal-5494	20	42	1	1	NUM
american_scientific_journal-5494	20	43	,	,	PUNCT
american_scientific_journal-5494	20	44	pp	pp	ADV
american_scientific_journal-5494	20	45	210	210	NUM
american_scientific_journal-5494	20	46	-	-	SYM
american_scientific_journal-5494	20	47	214	214	NUM
american_scientific_journal-5494	20	48	212	212	NUM
american_scientific_journal-5494	20	49	,	,	PUNCT
american_scientific_journal-5494	20	50	(	(	PUNCT
american_scientific_journal-5494	20	51	)	)	PUNCT
american_scientific_journal-5494	20	52	,	,	PUNCT
american_scientific_journal-5494	20	53	(	(	PUNCT
american_scientific_journal-5494	20	54	)	)	PUNCT
american_scientific_journal-5494	20	55	∫	∫	PROPN
american_scientific_journal-5494	20	56	(	(	PUNCT
american_scientific_journal-5494	20	57	)	)	PUNCT
american_scientific_journal-5494	20	58	(	(	PUNCT
american_scientific_journal-5494	20	59	)	)	PUNCT
american_scientific_journal-5494	20	60	(	(	PUNCT
american_scientific_journal-5494	20	61	)	)	PUNCT
american_scientific_journal-5494	20	62	the	the	PRON
american_scientific_journal-5494	20	63	(	(	PUNCT
american_scientific_journal-5494	20	64	)	)	PUNCT
american_scientific_journal-5494	20	65	is	be	AUX
american_scientific_journal-5494	20	66	the	the	DET
american_scientific_journal-5494	20	67	kernel	kernel	NOUN
american_scientific_journal-5494	20	68	of	of	ADP
american_scientific_journal-5494	20	69	transform	transform	NOUN
american_scientific_journal-5494	20	70	defined	define	VERB
american_scientific_journal-5494	20	71	in	in	ADP
american_scientific_journal-5494	20	72	[	[	X
american_scientific_journal-5494	20	73	6	6	NUM
american_scientific_journal-5494	20	74	]	]	PUNCT
american_scientific_journal-5494	20	75	(	(	PUNCT
american_scientific_journal-5494	20	76	)	)	PUNCT
american_scientific_journal-5494	20	77	{	{	PUNCT
american_scientific_journal-5494	20	78	(	(	PUNCT
american_scientific_journal-5494	20	79	)	)	PUNCT
american_scientific_journal-5494	20	80	.	.	PUNCT
american_scientific_journal-5494	21	1	/	/	PUNCT
american_scientific_journal-5494	21	2	(	(	PUNCT
american_scientific_journal-5494	21	3	)	)	PUNCT
american_scientific_journal-5494	21	4	(	(	PUNCT
american_scientific_journal-5494	21	5	)	)	PUNCT
american_scientific_journal-5494	21	6	(	(	PUNCT
american_scientific_journal-5494	21	7	)	)	PUNCT
american_scientific_journal-5494	21	8	(	(	PUNCT
american_scientific_journal-5494	21	9	5	5	NUM
american_scientific_journal-5494	21	10	)	)	PUNCT
american_scientific_journal-5494	21	11	where	where	SCONJ
american_scientific_journal-5494	21	12	(	(	PUNCT
american_scientific_journal-5494	21	13	)	)	PUNCT
american_scientific_journal-5494	21	14	√	√	INTJ
american_scientific_journal-5494	21	15	,	,	PUNCT
american_scientific_journal-5494	21	16	,	,	PUNCT
american_scientific_journal-5494	21	17	,	,	PUNCT
american_scientific_journal-5494	21	18	and	and	CCONJ
american_scientific_journal-5494	21	19	the	the	DET
american_scientific_journal-5494	21	20	inverse	inverse	NOUN
american_scientific_journal-5494	21	21	-	-	PUNCT
american_scientific_journal-5494	21	22	frft	frft	ADJ
american_scientific_journal-5494	21	23	with	with	ADP
american_scientific_journal-5494	21	24	respect	respect	NOUN
american_scientific_journal-5494	21	25	to	to	ADP
american_scientific_journal-5494	21	26	angle	angle	NOUN
american_scientific_journal-5494	21	27	is	be	AUX
american_scientific_journal-5494	21	28	the	the	DET
american_scientific_journal-5494	21	29	frft	frft	ADJ
american_scientific_journal-5494	21	30	with	with	ADP
american_scientific_journal-5494	21	31	angle	angle	NOUN
american_scientific_journal-5494	21	32	given	give	VERB
american_scientific_journal-5494	21	33	by	by	ADP
american_scientific_journal-5494	21	34	from	from	ADP
american_scientific_journal-5494	21	35	eqn	eqn	PROPN
american_scientific_journal-5494	21	36	(	(	PUNCT
american_scientific_journal-5494	21	37	4	4	NUM
american_scientific_journal-5494	21	38	)	)	PUNCT
american_scientific_journal-5494	21	39	is	be	AUX
american_scientific_journal-5494	21	40	(	(	PUNCT
american_scientific_journal-5494	21	41	)	)	PUNCT
american_scientific_journal-5494	21	42	∫	∫	PROPN
american_scientific_journal-5494	21	43	(	(	PUNCT
american_scientific_journal-5494	21	44	)	)	PUNCT
american_scientific_journal-5494	21	45	(	(	PUNCT
american_scientific_journal-5494	21	46	)	)	PUNCT
american_scientific_journal-5494	21	47	(	(	PUNCT
american_scientific_journal-5494	21	48	6	6	NUM
american_scientific_journal-5494	21	49	)	)	PUNCT
american_scientific_journal-5494	21	50	since	since	SCONJ
american_scientific_journal-5494	21	51	frft	frft	ADJ
american_scientific_journal-5494	21	52	is	be	AUX
american_scientific_journal-5494	21	53	the	the	DET
american_scientific_journal-5494	21	54	generalized	generalized	ADJ
american_scientific_journal-5494	21	55	form	form	NOUN
american_scientific_journal-5494	21	56	of	of	ADP
american_scientific_journal-5494	21	57	fourier	fourier	NOUN
american_scientific_journal-5494	21	58	transform	transform	NOUN
american_scientific_journal-5494	21	59	.	.	PUNCT
american_scientific_journal-5494	22	1	in	in	ADP
american_scientific_journal-5494	22	2	classical	classical	ADJ
american_scientific_journal-5494	22	3	fourier	fourier	NOUN
american_scientific_journal-5494	22	4	transform	transform	VERB
american_scientific_journal-5494	22	5	the	the	DET
american_scientific_journal-5494	22	6	concept	concept	NOUN
american_scientific_journal-5494	22	7	of	of	ADP
american_scientific_journal-5494	22	8	rotating	rotate	VERB
american_scientific_journal-5494	22	9	angle	angle	NOUN
american_scientific_journal-5494	22	10	is	be	AUX
american_scientific_journal-5494	22	11	where	where	SCONJ
american_scientific_journal-5494	22	12	in	in	ADP
american_scientific_journal-5494	22	13	frft	frft	ADJ
american_scientific_journal-5494	22	14	the	the	DET
american_scientific_journal-5494	22	15	concept	concept	NOUN
american_scientific_journal-5494	22	16	of	of	ADP
american_scientific_journal-5494	22	17	rotating	rotate	VERB
american_scientific_journal-5494	22	18	angleis	angleis	PROPN
american_scientific_journal-5494	22	19	generalized	generalize	VERB
american_scientific_journal-5494	22	20	to	to	ADP
american_scientific_journal-5494	22	21	over	over	ADP
american_scientific_journal-5494	22	22	an	an	DET
american_scientific_journal-5494	22	23	arbitrary	arbitrary	ADJ
american_scientific_journal-5494	22	24	angle	angle	NOUN
american_scientific_journal-5494	22	25	=	=	PUNCT
american_scientific_journal-5494	22	26	with	with	ADP
american_scientific_journal-5494	22	27	.	.	PUNCT
american_scientific_journal-5494	23	1	where	where	SCONJ
american_scientific_journal-5494	23	2	is	be	AUX
american_scientific_journal-5494	23	3	the	the	DET
american_scientific_journal-5494	23	4	order	order	NOUN
american_scientific_journal-5494	23	5	fractional	fractional	ADJ
american_scientific_journal-5494	23	6	fourier	fourier	NOUN
american_scientific_journal-5494	23	7	transform	transform	VERB
american_scientific_journal-5494	23	8	this	this	DET
american_scientific_journal-5494	23	9	frft	frft	ADJ
american_scientific_journal-5494	23	10	operator	operator	NOUN
american_scientific_journal-5494	23	11	shall	shall	AUX
american_scientific_journal-5494	23	12	be	be	AUX
american_scientific_journal-5494	23	13	denoted	denote	VERB
american_scientific_journal-5494	23	14	as	as	ADP
american_scientific_journal-5494	23	15	where	where	SCONJ
american_scientific_journal-5494	23	16	corresponds	correspond	VERB
american_scientific_journal-5494	23	17	to	to	ADP
american_scientific_journal-5494	23	18	the	the	DET
american_scientific_journal-5494	23	19	classical	classical	ADJ
american_scientific_journal-5494	23	20	ft	ft	NOUN
american_scientific_journal-5494	23	21	operator	operator	NOUN
american_scientific_journal-5494	23	22	over	over	ADP
american_scientific_journal-5494	23	23	rotational	rotational	ADJ
american_scientific_journal-5494	23	24	angle	angle	NOUN
american_scientific_journal-5494	23	25	,	,	PUNCT
american_scientific_journal-5494	23	26	therefore	therefore	ADV
american_scientific_journal-5494	23	27	it	it	PRON
american_scientific_journal-5494	23	28	is	be	AUX
american_scientific_journal-5494	23	29	similar	similar	ADJ
american_scientific_journal-5494	23	30	to	to	ADP
american_scientific_journal-5494	23	31	the	the	DET
american_scientific_journal-5494	23	32	fourier	fourier	NOUN
american_scientific_journal-5494	23	33	transform	transform	NOUN
american_scientific_journal-5494	23	34	whenever	whenever	SCONJ
american_scientific_journal-5494	23	35	the	the	DET
american_scientific_journal-5494	23	36	rotation	rotation	NOUN
american_scientific_journal-5494	23	37	of	of	ADP
american_scientific_journal-5494	23	38	angle	angle	NOUN
american_scientific_journal-5494	23	39	is	be	AUX
american_scientific_journal-5494	23	40	,	,	PUNCT
american_scientific_journal-5494	23	41	for	for	ADP
american_scientific_journal-5494	23	42	then	then	ADV
american_scientific_journal-5494	23	43	represent	represent	VERB
american_scientific_journal-5494	23	44	the	the	DET
american_scientific_journal-5494	23	45	axis	axis	NOUN
american_scientific_journal-5494	23	46	as	as	SCONJ
american_scientific_journal-5494	23	47	the	the	DET
american_scientific_journal-5494	23	48	reverese	reverese	ADJ
american_scientific_journal-5494	23	49	time	time	NOUN
american_scientific_journal-5494	23	50	axix	axix	NOUN
american_scientific_journal-5494	23	51	known	know	VERB
american_scientific_journal-5494	23	52	as	as	ADP
american_scientific_journal-5494	23	53	the	the	DET
american_scientific_journal-5494	23	54	parity	parity	NOUN
american_scientific_journal-5494	23	55	operator	operator	NOUN
american_scientific_journal-5494	23	56	,	,	PUNCT
american_scientific_journal-5494	23	57	i.e.	i.e.	X
american_scientific_journal-5494	23	58	,	,	PUNCT
american_scientific_journal-5494	23	59	the	the	DET
american_scientific_journal-5494	23	60	time	time	NOUN
american_scientific_journal-5494	23	61	axis	axis	NOUN
american_scientific_journal-5494	23	62	rotated	rotate	VERB
american_scientific_journal-5494	23	63	over	over	ADP
american_scientific_journal-5494	23	64	an	an	DET
american_scientific_journal-5494	23	65	angle	angle	NOUN
american_scientific_journal-5494	23	66	,	,	PUNCT
american_scientific_journal-5494	23	67	for	for	ADP
american_scientific_journal-5494	23	68	the	the	DET
american_scientific_journal-5494	23	69	rotation	rotation	NOUN
american_scientific_journal-5494	23	70	of	of	ADP
american_scientific_journal-5494	23	71	the	the	DET
american_scientific_journal-5494	23	72	axis	axis	NOUN
american_scientific_journal-5494	23	73	over	over	ADP
american_scientific_journal-5494	23	74	an	an	DET
american_scientific_journal-5494	23	75	angle	angle	NOUN
american_scientific_journal-5494	23	76	or	or	CCONJ
american_scientific_journal-5494	23	77	which	which	PRON
american_scientific_journal-5494	23	78	represent	represent	VERB
american_scientific_journal-5494	23	79	the	the	DET
american_scientific_journal-5494	23	80	inversion	inversion	NOUN
american_scientific_journal-5494	23	81	fourier	fourier	NOUN
american_scientific_journal-5494	23	82	transform	transform	NOUN
american_scientific_journal-5494	23	83	,	,	PUNCT
american_scientific_journal-5494	23	84	i.e.	i.e.	X
american_scientific_journal-5494	23	85	,	,	PUNCT
american_scientific_journal-5494	23	86	.	.	PUNCT
american_scientific_journal-5494	24	1	it	it	PRON
american_scientific_journal-5494	24	2	will	will	AUX
american_scientific_journal-5494	24	3	now	now	ADV
american_scientific_journal-5494	24	4	be	be	AUX
american_scientific_journal-5494	24	5	clear	clear	ADJ
american_scientific_journal-5494	24	6	that	that	SCONJ
american_scientific_journal-5494	24	7	by	by	ADP
american_scientific_journal-5494	24	8	another	another	DET
american_scientific_journal-5494	24	9	rotation	rotation	NOUN
american_scientific_journal-5494	24	10	of	of	ADP
american_scientific_journal-5494	24	11	angle	angle	NOUN
american_scientific_journal-5494	24	12	,	,	PUNCT
american_scientific_journal-5494	24	13	i.e.	i.e.	X
american_scientific_journal-5494	24	14	,	,	PUNCT
american_scientific_journal-5494	24	15	and	and	CCONJ
american_scientific_journal-5494	24	16	,	,	PUNCT
american_scientific_journal-5494	24	17	which	which	PRON
american_scientific_journal-5494	24	18	brings	bring	VERB
american_scientific_journal-5494	24	19	us	we	PRON
american_scientific_journal-5494	24	20	back	back	ADV
american_scientific_journal-5494	24	21	to	to	ADP
american_scientific_journal-5494	24	22	the	the	DET
american_scientific_journal-5494	24	23	original	original	ADJ
american_scientific_journal-5494	24	24	time	time	NOUN
american_scientific_journal-5494	24	25	axis	axis	NOUN
american_scientific_journal-5494	24	26	,	,	PUNCT
american_scientific_journal-5494	24	27	hence	hence	ADV
american_scientific_journal-5494	24	28	[	[	X
american_scientific_journal-5494	24	29	6	6	NUM
american_scientific_journal-5494	24	30	]	]	PUNCT
american_scientific_journal-5494	24	31	.	.	PUNCT
american_scientific_journal-5494	25	1	2.2	2.2	NUM
american_scientific_journal-5494	25	2	.	.	PUNCT
american_scientific_journal-5494	26	1	two	two	NUM
american_scientific_journal-5494	26	2	dimensional	dimensional	ADJ
american_scientific_journal-5494	26	3	fractional	fractional	ADJ
american_scientific_journal-5494	26	4	fourier	fourier	NOUN
american_scientific_journal-5494	26	5	transform	transform	VERB
american_scientific_journal-5494	26	6	tin	tin	NOUN
american_scientific_journal-5494	26	7	two	two	NUM
american_scientific_journal-5494	26	8	-	-	PUNCT
american_scientific_journal-5494	26	9	dimensional	dimensional	ADJ
american_scientific_journal-5494	26	10	(	(	PUNCT
american_scientific_journal-5494	26	11	2d)-fractional	2d)-fractional	NUM
american_scientific_journal-5494	26	12	fourier	fourier	NOUN
american_scientific_journal-5494	26	13	transform	transform	NOUN
american_scientific_journal-5494	26	14	that	that	PRON
american_scientific_journal-5494	26	15	is	be	AUX
american_scientific_journal-5494	26	16	extension	extension	NOUN
american_scientific_journal-5494	26	17	of	of	ADP
american_scientific_journal-5494	26	18	equation	equation	NOUN
american_scientific_journal-5494	26	19	(	(	PUNCT
american_scientific_journal-5494	26	20	4	4	NUM
american_scientific_journal-5494	26	21	)	)	PUNCT
american_scientific_journal-5494	26	22	with	with	ADP
american_scientific_journal-5494	26	23	two	two	NUM
american_scientific_journal-5494	26	24	variable	variable	NOUN
american_scientific_journal-5494	26	25	and	and	CCONJ
american_scientific_journal-5494	26	26	with	with	ADP
american_scientific_journal-5494	26	27	two	two	NUM
american_scientific_journal-5494	26	28	angles	angle	NOUN
american_scientific_journal-5494	26	29	it	it	PRON
american_scientific_journal-5494	26	30	is	be	AUX
american_scientific_journal-5494	26	31	denoted	denote	VERB
american_scientific_journal-5494	26	32	as	as	ADP
american_scientific_journal-5494	26	33	*	*	PUNCT
american_scientific_journal-5494	26	34	(	(	PUNCT
american_scientific_journal-5494	26	35	)	)	PUNCT
american_scientific_journal-5494	26	36	+	+	NUM
american_scientific_journal-5494	26	37	*	*	PUNCT
american_scientific_journal-5494	26	38	(	(	PUNCT
american_scientific_journal-5494	26	39	)	)	PUNCT
american_scientific_journal-5494	26	40	+	+	ADJ
american_scientific_journal-5494	26	41	(	(	PUNCT
american_scientific_journal-5494	26	42	)	)	PUNCT
american_scientific_journal-5494	26	43	(	(	PUNCT
american_scientific_journal-5494	26	44	)	)	PUNCT
american_scientific_journal-5494	26	45	∫	∫	PROPN
american_scientific_journal-5494	26	46	∫	∫	PROPN
american_scientific_journal-5494	26	47	(	(	PUNCT
american_scientific_journal-5494	26	48	)	)	PUNCT
american_scientific_journal-5494	26	49	(	(	PUNCT
american_scientific_journal-5494	26	50	)	)	PUNCT
american_scientific_journal-5494	26	51	(	(	PUNCT
american_scientific_journal-5494	26	52	)	)	PUNCT
american_scientific_journal-5494	27	1	where	where	SCONJ
american_scientific_journal-5494	27	2	(	(	PUNCT
american_scientific_journal-5494	27	3	)	)	PUNCT
american_scientific_journal-5494	27	4	(	(	PUNCT
american_scientific_journal-5494	27	5	)	)	PUNCT
american_scientific_journal-5494	27	6	(	(	PUNCT
american_scientific_journal-5494	27	7	)	)	PUNCT
american_scientific_journal-5494	27	8	and	and	CCONJ
american_scientific_journal-5494	27	9	defined	define	VERB
american_scientific_journal-5494	27	10	(	(	PUNCT
american_scientific_journal-5494	27	11	)	)	PUNCT
american_scientific_journal-5494	27	12	(	(	PUNCT
american_scientific_journal-5494	27	13	)	)	PUNCT
american_scientific_journal-5494	27	14	{	{	PUNCT
american_scientific_journal-5494	27	15	.	.	PUNCT
american_scientific_journal-5494	27	16	/	/	PUNCT
american_scientific_journal-5494	27	17	.	.	PUNCT
american_scientific_journal-5494	27	18	/	/	PUNCT
american_scientific_journal-5494	27	19	}	}	PUNCT
american_scientific_journal-5494	27	20	(	(	PUNCT
american_scientific_journal-5494	27	21	)	)	PUNCT
american_scientific_journal-5494	27	22	american	american	ADJ
american_scientific_journal-5494	27	23	scientific	scientific	ADJ
american_scientific_journal-5494	27	24	research	research	NOUN
american_scientific_journal-5494	27	25	journal	journal	NOUN
american_scientific_journal-5494	27	26	for	for	ADP
american_scientific_journal-5494	27	27	engineering	engineering	NOUN
american_scientific_journal-5494	27	28	,	,	PUNCT
american_scientific_journal-5494	27	29	technology	technology	NOUN
american_scientific_journal-5494	27	30	,	,	PUNCT
american_scientific_journal-5494	27	31	and	and	CCONJ
american_scientific_journal-5494	27	32	sciences	science	NOUN
american_scientific_journal-5494	27	33	(	(	PUNCT
american_scientific_journal-5494	27	34	asrjets	asrjet	NOUN
american_scientific_journal-5494	27	35	)	)	PUNCT
american_scientific_journal-5494	27	36	(	(	PUNCT
american_scientific_journal-5494	27	37	2019	2019	NUM
american_scientific_journal-5494	27	38	)	)	PUNCT
american_scientific_journal-5494	27	39	volume	volume	NOUN
american_scientific_journal-5494	27	40	62	62	NUM
american_scientific_journal-5494	27	41	,	,	PUNCT
american_scientific_journal-5494	27	42	no	no	DET
american_scientific_journal-5494	27	43	1	1	NUM
american_scientific_journal-5494	27	44	,	,	PUNCT
american_scientific_journal-5494	27	45	pp	pp	ADV
american_scientific_journal-5494	27	46	210	210	NUM
american_scientific_journal-5494	27	47	-	-	SYM
american_scientific_journal-5494	27	48	214	214	NUM
american_scientific_journal-5494	27	49	213	213	NUM
american_scientific_journal-5494	27	50	since	since	SCONJ
american_scientific_journal-5494	27	51	two	two	NUM
american_scientific_journal-5494	27	52	dimensional	dimensional	ADJ
american_scientific_journal-5494	27	53	fractional	fractional	ADJ
american_scientific_journal-5494	27	54	fourier	fourier	NOUN
american_scientific_journal-5494	27	55	transform	transform	NOUN
american_scientific_journal-5494	27	56	is	be	AUX
american_scientific_journal-5494	27	57	the	the	DET
american_scientific_journal-5494	27	58	generalized	generalized	ADJ
american_scientific_journal-5494	27	59	form	form	NOUN
american_scientific_journal-5494	27	60	of	of	ADP
american_scientific_journal-5494	27	61	two	two	NUM
american_scientific_journal-5494	27	62	dimensional	dimensional	ADJ
american_scientific_journal-5494	27	63	(	(	PUNCT
american_scientific_journal-5494	27	64	2	2	NUM
american_scientific_journal-5494	27	65	-	-	SYM
american_scientific_journal-5494	27	66	d	d	NOUN
american_scientific_journal-5494	27	67	)	)	PUNCT
american_scientific_journal-5494	27	68	classical	classical	ADJ
american_scientific_journal-5494	27	69	fourier	fourier	NOUN
american_scientific_journal-5494	27	70	transform	transform	NOUN
american_scientific_journal-5494	27	71	if	if	SCONJ
american_scientific_journal-5494	27	72	two	two	NUM
american_scientific_journal-5494	27	73	angles	angle	NOUN
american_scientific_journal-5494	27	74	of	of	ADP
american_scientific_journal-5494	27	75	rotation	rotation	NOUN
american_scientific_journal-5494	27	76	replaced	replace	VERB
american_scientific_journal-5494	27	77	by	by	ADP
american_scientific_journal-5494	27	78	n	n	PRON
american_scientific_journal-5494	27	79	it	it	PRON
american_scientific_journal-5494	27	80	will	will	AUX
american_scientific_journal-5494	27	81	reduce	reduce	VERB
american_scientific_journal-5494	27	82	the(2	the(2	NOUN
american_scientific_journal-5494	27	83	-	-	PUNCT
american_scientific_journal-5494	27	84	d)ft	d)ft	PROPN
american_scientific_journal-5494	27	85	with	with	ADP
american_scientific_journal-5494	27	86	same	same	ADJ
american_scientific_journal-5494	27	87	rotational	rotational	ADJ
american_scientific_journal-5494	27	88	axis	axis	NOUN
american_scientific_journal-5494	27	89	properties	property	NOUN
american_scientific_journal-5494	27	90	.	.	PUNCT
american_scientific_journal-5494	28	1	if	if	SCONJ
american_scientific_journal-5494	28	2	one	one	NUM
american_scientific_journal-5494	28	3	of	of	ADP
american_scientific_journal-5494	28	4	these	these	DET
american_scientific_journal-5494	28	5	angle	angle	NOUN
american_scientific_journal-5494	28	6	is	be	AUX
american_scientific_journal-5494	28	7	zero	zero	NUM
american_scientific_journal-5494	28	8	,	,	PUNCT
american_scientific_journal-5494	28	9	then	then	ADV
american_scientific_journal-5494	28	10	(	(	PUNCT
american_scientific_journal-5494	28	11	2	2	NUM
american_scientific_journal-5494	28	12	-	-	SYM
american_scientific_journal-5494	28	13	d	d	NOUN
american_scientific_journal-5494	28	14	)	)	PUNCT
american_scientific_journal-5494	28	15	frft	frft	ADJ
american_scientific_journal-5494	28	16	reduced	reduce	VERB
american_scientific_journal-5494	28	17	to	to	ADP
american_scientific_journal-5494	28	18	(	(	PUNCT
american_scientific_journal-5494	28	19	1	1	NUM
american_scientific_journal-5494	28	20	-	-	SYM
american_scientific_journal-5494	28	21	d	d	NOUN
american_scientific_journal-5494	28	22	)	)	PUNCT
american_scientific_journal-5494	28	23	frft	frft	ADJ
american_scientific_journal-5494	28	24	.	.	PUNCT
american_scientific_journal-5494	29	1	2.3	2.3	NUM
american_scientific_journal-5494	29	2	.	.	PUNCT
american_scientific_journal-5494	30	1	ndimensional	ndimensional	ADJ
american_scientific_journal-5494	30	2	fractional	fractional	ADJ
american_scientific_journal-5494	30	3	fourier	fourier	NOUN
american_scientific_journal-5494	30	4	transform	transform	NOUN
american_scientific_journal-5494	30	5	in	in	ADP
american_scientific_journal-5494	30	6	a	a	DET
american_scientific_journal-5494	30	7	similar	similar	ADJ
american_scientific_journal-5494	30	8	manner	manner	NOUN
american_scientific_journal-5494	30	9	equation	equation	NOUN
american_scientific_journal-5494	30	10	(	(	PUNCT
american_scientific_journal-5494	30	11	6	6	NUM
american_scientific_journal-5494	30	12	)	)	PUNCT
american_scientific_journal-5494	30	13	can	can	AUX
american_scientific_journal-5494	30	14	be	be	AUX
american_scientific_journal-5494	30	15	extended	extend	VERB
american_scientific_journal-5494	30	16	to	to	ADP
american_scientific_journal-5494	30	17	3	3	NUM
american_scientific_journal-5494	30	18	-	-	SYM
american_scientific_journal-5494	30	19	d	d	NOUN
american_scientific_journal-5494	30	20	and	and	CCONJ
american_scientific_journal-5494	30	21	so	so	ADV
american_scientific_journal-5494	30	22	on	on	ADP
american_scientific_journal-5494	30	23	up	up	ADP
american_scientific_journal-5494	30	24	to	to	ADP
american_scientific_journal-5494	30	25	n	n	CCONJ
american_scientific_journal-5494	30	26	-	-	PUNCT
american_scientific_journal-5494	30	27	dimensional	dimensional	ADJ
american_scientific_journal-5494	30	28	fractional	fractional	ADJ
american_scientific_journal-5494	30	29	fourier	fourier	NOUN
american_scientific_journal-5494	30	30	transform	transform	NOUN
american_scientific_journal-5494	30	31	.	.	PUNCT
american_scientific_journal-5494	31	1	let	let	VERB
american_scientific_journal-5494	31	2	us	we	PRON
american_scientific_journal-5494	31	3	consider	consider	VERB
american_scientific_journal-5494	31	4	a	a	DET
american_scientific_journal-5494	31	5	function	function	NOUN
american_scientific_journal-5494	31	6	with	with	ADP
american_scientific_journal-5494	31	7	n	n	NOUN
american_scientific_journal-5494	31	8	variables	variable	NOUN
american_scientific_journal-5494	31	9	and	and	CCONJ
american_scientific_journal-5494	31	10	with	with	ADP
american_scientific_journal-5494	31	11	n	n	CCONJ
american_scientific_journal-5494	31	12	rotational	rotational	ADJ
american_scientific_journal-5494	31	13	angles	angle	NOUN
american_scientific_journal-5494	31	14	the	the	DET
american_scientific_journal-5494	31	15	frftcan	frftcan	ADJ
american_scientific_journal-5494	31	16	be	be	AUX
american_scientific_journal-5494	31	17	denoted	denote	VERB
american_scientific_journal-5494	31	18	and	and	CCONJ
american_scientific_journal-5494	31	19	defined	define	VERB
american_scientific_journal-5494	31	20	defined	define	VERB
american_scientific_journal-5494	31	21	as	as	SCONJ
american_scientific_journal-5494	31	22	follows	follow	VERB
american_scientific_journal-5494	31	23	*	*	PUNCT
american_scientific_journal-5494	31	24	(	(	PUNCT
american_scientific_journal-5494	31	25	)	)	PUNCT
american_scientific_journal-5494	32	1	+	+	NUM
american_scientific_journal-5494	32	2	*	*	PUNCT
american_scientific_journal-5494	32	3	(	(	PUNCT
american_scientific_journal-5494	32	4	)	)	PUNCT
american_scientific_journal-5494	32	5	+	+	ADJ
american_scientific_journal-5494	32	6	(	(	PUNCT
american_scientific_journal-5494	32	7	)	)	PUNCT
american_scientific_journal-5494	32	8	(	(	PUNCT
american_scientific_journal-5494	32	9	)	)	PUNCT
american_scientific_journal-5494	32	10	∫	∫	PROPN
american_scientific_journal-5494	32	11	∫	∫	PROPN
american_scientific_journal-5494	32	12	(	(	PUNCT
american_scientific_journal-5494	32	13	)	)	PUNCT
american_scientific_journal-5494	32	14	(	(	PUNCT
american_scientific_journal-5494	32	15	)	)	PUNCT
american_scientific_journal-5494	32	16	(	(	PUNCT
american_scientific_journal-5494	32	17	)	)	PUNCT
american_scientific_journal-5494	32	18	where	where	SCONJ
american_scientific_journal-5494	32	19	(	(	PUNCT
american_scientific_journal-5494	32	20	)	)	PUNCT
american_scientific_journal-5494	32	21	(	(	PUNCT
american_scientific_journal-5494	32	22	)	)	PUNCT
american_scientific_journal-5494	32	23	{	{	PUNCT
american_scientific_journal-5494	32	24	(	(	PUNCT
american_scientific_journal-5494	32	25	)	)	PUNCT
american_scientific_journal-5494	32	26	(	(	PUNCT
american_scientific_journal-5494	32	27	)	)	PUNCT
american_scientific_journal-5494	32	28	(	(	PUNCT
american_scientific_journal-5494	32	29	)	)	PUNCT
american_scientific_journal-5494	32	30	}	}	PUNCT
american_scientific_journal-5494	32	31	(	(	PUNCT
american_scientific_journal-5494	32	32	)	)	PUNCT
american_scientific_journal-5494	32	33	the	the	DET
american_scientific_journal-5494	32	34	ndimensional	ndimensional	ADJ
american_scientific_journal-5494	32	35	fractional	fractional	ADJ
american_scientific_journal-5494	32	36	fourier	fourier	NOUN
american_scientific_journal-5494	32	37	transform	transform	NOUN
american_scientific_journal-5494	32	38	is	be	AUX
american_scientific_journal-5494	32	39	the	the	DET
american_scientific_journal-5494	32	40	generalized	generalized	ADJ
american_scientific_journal-5494	32	41	form	form	NOUN
american_scientific_journal-5494	32	42	of	of	ADP
american_scientific_journal-5494	32	43	ndimensional	ndimensional	ADJ
american_scientific_journal-5494	32	44	classical	classical	ADJ
american_scientific_journal-5494	32	45	fourier	fourier	NOUN
american_scientific_journal-5494	32	46	transform	transform	NOUN
american_scientific_journal-5494	32	47	if	if	SCONJ
american_scientific_journal-5494	32	48	n	n	CCONJ
american_scientific_journal-5494	32	49	-	-	PUNCT
american_scientific_journal-5494	32	50	angles	angle	NOUN
american_scientific_journal-5494	32	51	of	of	ADP
american_scientific_journal-5494	32	52	rotation	rotation	NOUN
american_scientific_journal-5494	32	53	replaced	replace	VERB
american_scientific_journal-5494	32	54	by	by	ADP
american_scientific_journal-5494	32	55	furthe	furthe	NOUN
american_scientific_journal-5494	32	56	if	if	SCONJ
american_scientific_journal-5494	32	57	each	each	DET
american_scientific_journal-5494	32	58	rotational	rotational	ADJ
american_scientific_journal-5494	32	59	angle	angle	NOUN
american_scientific_journal-5494	32	60	is	be	AUX
american_scientific_journal-5494	32	61	rotated	rotate	VERB
american_scientific_journal-5494	32	62	over	over	ADP
american_scientific_journal-5494	32	63	an	an	DET
american_scientific_journal-5494	32	64	angle	angle	NOUN
american_scientific_journal-5494	32	65	it	it	PRON
american_scientific_journal-5494	32	66	will	will	AUX
american_scientific_journal-5494	32	67	posses	posse	VERB
american_scientific_journal-5494	32	68	the	the	DET
american_scientific_journal-5494	32	69	same	same	ADJ
american_scientific_journal-5494	32	70	roatational	roatational	ADJ
american_scientific_journal-5494	32	71	properties	property	NOUN
american_scientific_journal-5494	32	72	of	of	ADP
american_scientific_journal-5494	32	73	n	n	CCONJ
american_scientific_journal-5494	32	74	-	-	PUNCT
american_scientific_journal-5494	32	75	d	d	NOUN
american_scientific_journal-5494	32	76	fourier	fourier	NOUN
american_scientific_journal-5494	32	77	transform	transform	NOUN
american_scientific_journal-5494	32	78	.	.	PUNCT
american_scientific_journal-5494	33	1	if	if	SCONJ
american_scientific_journal-5494	33	2	one	one	NUM
american_scientific_journal-5494	33	3	of	of	ADP
american_scientific_journal-5494	33	4	these	these	DET
american_scientific_journal-5494	33	5	angle	angle	NOUN
american_scientific_journal-5494	33	6	is	be	AUX
american_scientific_journal-5494	33	7	zero	zero	NUM
american_scientific_journal-5494	33	8	,	,	PUNCT
american_scientific_journal-5494	33	9	then	then	ADV
american_scientific_journal-5494	33	10	n	n	CCONJ
american_scientific_journal-5494	33	11	-	-	PUNCT
american_scientific_journal-5494	33	12	d	d	ADV
american_scientific_journal-5494	33	13	frft	frft	ADJ
american_scientific_journal-5494	33	14	reduced	reduce	VERB
american_scientific_journal-5494	33	15	to	to	ADP
american_scientific_journal-5494	33	16	(	(	PUNCT
american_scientific_journal-5494	33	17	n-1	n-1	ADV
american_scientific_journal-5494	33	18	)	)	PUNCT
american_scientific_journal-5494	33	19	dimensional	dimensional	ADJ
american_scientific_journal-5494	33	20	frft	frft	ADJ
american_scientific_journal-5494	33	21	.	.	PUNCT
american_scientific_journal-5494	34	1	2.4	2.4	NUM
american_scientific_journal-5494	34	2	.	.	PUNCT
american_scientific_journal-5494	35	1	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	35	2	and	and	CCONJ
american_scientific_journal-5494	35	3	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	35	4	the	the	DET
american_scientific_journal-5494	35	5	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-5494	35	6	of	of	ADP
american_scientific_journal-5494	35	7	the	the	DET
american_scientific_journal-5494	35	8	fractional	fractional	ADJ
american_scientific_journal-5494	35	9	fourier	fourier	NOUN
american_scientific_journal-5494	35	10	transform	transform	NOUN
american_scientific_journal-5494	35	11	are	be	AUX
american_scientific_journal-5494	35	12	the	the	DET
american_scientific_journal-5494	35	13	hermite	hermite	ADJ
american_scientific_journal-5494	35	14	functions	function	NOUN
american_scientific_journal-5494	35	15	which	which	PRON
american_scientific_journal-5494	35	16	is	be	AUX
american_scientific_journal-5494	35	17	same	same	ADJ
american_scientific_journal-5494	35	18	as	as	ADP
american_scientific_journal-5494	35	19	for	for	ADP
american_scientific_journal-5494	35	20	classical	classical	ADJ
american_scientific_journal-5494	35	21	n	n	CCONJ
american_scientific_journal-5494	35	22	-	-	PUNCT
american_scientific_journal-5494	35	23	dimensional	dimensional	ADJ
american_scientific_journal-5494	35	24	fourier	fourier	NOUN
american_scientific_journal-5494	35	25	transform	transform	NOUN
american_scientific_journal-5494	35	26	also	also	ADV
american_scientific_journal-5494	35	27	hold	hold	VERB
american_scientific_journal-5494	35	28	eqn	eqn	NOUN
american_scientific_journal-5494	35	29	(	(	PUNCT
american_scientific_journal-5494	35	30	3	3	NUM
american_scientific_journal-5494	35	31	)	)	PUNCT
american_scientific_journal-5494	35	32	and	and	CCONJ
american_scientific_journal-5494	35	33	the	the	DET
american_scientific_journal-5494	35	34	corresponding	corresponding	ADJ
american_scientific_journal-5494	35	35	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	35	36	are	be	AUX
american_scientific_journal-5494	35	37	(	(	PUNCT
american_scientific_journal-5494	35	38	)	)	PUNCT
american_scientific_journal-5494	35	39	if	if	SCONJ
american_scientific_journal-5494	35	40	we	we	PRON
american_scientific_journal-5494	35	41	put	put	VERB
american_scientific_journal-5494	35	42	leads	lead	VERB
american_scientific_journal-5494	35	43	to	to	ADP
american_scientific_journal-5494	35	44	identity	identity	NOUN
american_scientific_journal-5494	35	45	operator	operator	NOUN
american_scientific_journal-5494	35	46	and	and	CCONJ
american_scientific_journal-5494	35	47	we	we	PRON
american_scientific_journal-5494	35	48	take	take	VERB
american_scientific_journal-5494	35	49	the	the	DET
american_scientific_journal-5494	35	50	result	result	NOUN
american_scientific_journal-5494	35	51	leads	lead	VERB
american_scientific_journal-5494	35	52	to	to	ADP
american_scientific_journal-5494	35	53	the	the	DET
american_scientific_journal-5494	35	54	parity	parity	NOUN
american_scientific_journal-5494	35	55	operator	operator	NOUN
american_scientific_journal-5494	35	56	.	.	PUNCT
american_scientific_journal-5494	36	1	if	if	SCONJ
american_scientific_journal-5494	36	2	we	we	PRON
american_scientific_journal-5494	36	3	define	define	VERB
american_scientific_journal-5494	36	4	the	the	DET
american_scientific_journal-5494	36	5	order	order	NOUN
american_scientific_journal-5494	36	6	n	n	PROPN
american_scientific_journal-5494	36	7	of	of	ADP
american_scientific_journal-5494	36	8	the	the	DET
american_scientific_journal-5494	36	9	fractional	fractional	ADJ
american_scientific_journal-5494	36	10	fourier	fourier	NOUN
american_scientific_journal-5494	36	11	transform	transform	NOUN
american_scientific_journal-5494	36	12	by	by	ADP
american_scientific_journal-5494	36	13	(	(	PUNCT
american_scientific_journal-5494	36	14	)	)	PUNCT
american_scientific_journal-5494	36	15	we	we	PRON
american_scientific_journal-5494	36	16	see	see	VERB
american_scientific_journal-5494	36	17	that	that	SCONJ
american_scientific_journal-5494	36	18	the	the	DET
american_scientific_journal-5494	36	19	regular	regular	ADJ
american_scientific_journal-5494	36	20	fourier	fourier	NOUN
american_scientific_journal-5494	36	21	transform	transform	NOUN
american_scientific_journal-5494	36	22	is	be	AUX
american_scientific_journal-5494	36	23	of	of	ADP
american_scientific_journal-5494	36	24	order	order	NOUN
american_scientific_journal-5494	36	25	1	1	NUM
american_scientific_journal-5494	36	26	.	.	PUNCT
american_scientific_journal-5494	37	1	order	order	NOUN
american_scientific_journal-5494	37	2	0	0	NUM
american_scientific_journal-5494	37	3	is	be	AUX
american_scientific_journal-5494	37	4	the	the	DET
american_scientific_journal-5494	37	5	identity	identity	NOUN
american_scientific_journal-5494	37	6	operation	operation	NOUN
american_scientific_journal-5494	37	7	and	and	CCONJ
american_scientific_journal-5494	37	8	order	order	NOUN
american_scientific_journal-5494	37	9	2	2	NUM
american_scientific_journal-5494	37	10	is	be	AUX
american_scientific_journal-5494	37	11	the	the	DET
american_scientific_journal-5494	37	12	parity	parity	NOUN
american_scientific_journal-5494	37	13	transformation	transformation	NOUN
american_scientific_journal-5494	37	14	.	.	PUNCT
american_scientific_journal-5494	38	1	negative	negative	ADJ
american_scientific_journal-5494	38	2	orders	order	NOUN
american_scientific_journal-5494	38	3	correspond	correspond	VERB
american_scientific_journal-5494	38	4	to	to	ADP
american_scientific_journal-5494	38	5	inverse	inverse	NOUN
american_scientific_journal-5494	38	6	transforms	transform	NOUN
american_scientific_journal-5494	38	7	.	.	PUNCT
american_scientific_journal-5494	39	1	the	the	DET
american_scientific_journal-5494	39	2	whole	whole	ADJ
american_scientific_journal-5494	39	3	range	range	NOUN
american_scientific_journal-5494	39	4	of	of	ADP
american_scientific_journal-5494	39	5	transforms	transform	NOUN
american_scientific_journal-5494	39	6	is	be	AUX
american_scientific_journal-5494	39	7	covered	cover	VERB
american_scientific_journal-5494	39	8	by	by	ADP
american_scientific_journal-5494	39	9	the	the	DET
american_scientific_journal-5494	39	10	orders	order	NOUN
american_scientific_journal-5494	39	11	—	—	PUNCT
american_scientific_journal-5494	39	12	.	.	PUNCT
american_scientific_journal-5494	40	1	transforms	transform	VERB
american_scientific_journal-5494	40	2	with	with	ADP
american_scientific_journal-5494	40	3	non	non	ADJ
american_scientific_journal-5494	40	4	-	-	ADJ
american_scientific_journal-5494	40	5	integral	integral	ADJ
american_scientific_journal-5494	40	6	values	value	NOUN
american_scientific_journal-5494	40	7	of	of	ADP
american_scientific_journal-5494	40	8	n	n	PRON
american_scientific_journal-5494	40	9	may	may	AUX
american_scientific_journal-5494	40	10	be	be	AUX
american_scientific_journal-5494	40	11	called	call	VERB
american_scientific_journal-5494	40	12	fourier	fourier	NOUN
american_scientific_journal-5494	40	13	transforms	transform	NOUN
american_scientific_journal-5494	40	14	of	of	ADP
american_scientific_journal-5494	40	15	fractional	fractional	ADJ
american_scientific_journal-5494	40	16	order	order	NOUN
american_scientific_journal-5494	40	17	.	.	PUNCT
american_scientific_journal-5494	41	1	thus	thus	ADV
american_scientific_journal-5494	41	2	we	we	PRON
american_scientific_journal-5494	41	3	can	can	AUX
american_scientific_journal-5494	41	4	define	define	VERB
american_scientific_journal-5494	41	5	the	the	DET
american_scientific_journal-5494	41	6	eigen	eigen	PROPN
american_scientific_journal-5494	41	7	values	value	NOUN
american_scientific_journal-5494	41	8	for	for	ADP
american_scientific_journal-5494	41	9	the	the	DET
american_scientific_journal-5494	41	10	n	n	CCONJ
american_scientific_journal-5494	41	11	-	-	PUNCT
american_scientific_journal-5494	41	12	d	d	NOUN
american_scientific_journal-5494	41	13	fractional	fractional	ADJ
american_scientific_journal-5494	41	14	fourier	fourier	NOUN
american_scientific_journal-5494	41	15	transform	transform	NOUN
american_scientific_journal-5494	41	16	as	as	ADP
american_scientific_journal-5494	41	17	(	(	PUNCT
american_scientific_journal-5494	41	18	(	(	PUNCT
american_scientific_journal-5494	41	19	)	)	PUNCT
american_scientific_journal-5494	41	20	)	)	PUNCT
american_scientific_journal-5494	41	21	,	,	PUNCT
american_scientific_journal-5494	41	22	where	where	SCONJ
american_scientific_journal-5494	41	23	if	if	SCONJ
american_scientific_journal-5494	41	24	we	we	PRON
american_scientific_journal-5494	41	25	consider	consider	VERB
american_scientific_journal-5494	41	26	then	then	ADV
american_scientific_journal-5494	41	27	it	it	PRON
american_scientific_journal-5494	41	28	will	will	AUX
american_scientific_journal-5494	41	29	be	be	AUX
american_scientific_journal-5494	41	30	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	41	31	of	of	ADP
american_scientific_journal-5494	41	32	i	i	PROPN
american_scientific_journal-5494	41	33	-	-	PUNCT
american_scientific_journal-5494	41	34	d	d	PROPN
american_scientific_journal-5494	41	35	fractional	fractional	ADJ
american_scientific_journal-5494	41	36	fourier	fourier	NOUN
american_scientific_journal-5494	41	37	transform	transform	NOUN
american_scientific_journal-5494	41	38	where	where	SCONJ
american_scientific_journal-5494	41	39	for	for	ADP
american_scientific_journal-5494	41	40	then	then	ADV
american_scientific_journal-5494	41	41	it	it	PRON
american_scientific_journal-5494	41	42	will	will	AUX
american_scientific_journal-5494	41	43	eigenvalues	eigenvalues	VERB
american_scientific_journal-5494	41	44	of	of	ADP
american_scientific_journal-5494	41	45	2	2	NUM
american_scientific_journal-5494	41	46	-	-	PUNCT
american_scientific_journal-5494	41	47	d	d	NOUN
american_scientific_journal-5494	41	48	fractional	fractional	ADJ
american_scientific_journal-5494	41	49	fourier	fourier	NOUN
american_scientific_journal-5494	41	50	transform	transform	VERB
american_scientific_journal-5494	41	51	ain	ain	NOUN
american_scientific_journal-5494	41	52	this	this	DET
american_scientific_journal-5494	41	53	case	case	NOUN
american_scientific_journal-5494	41	54	american	american	PROPN
american_scientific_journal-5494	41	55	scientific	scientific	ADJ
american_scientific_journal-5494	41	56	research	research	NOUN
american_scientific_journal-5494	41	57	journal	journal	NOUN
american_scientific_journal-5494	41	58	for	for	ADP
american_scientific_journal-5494	41	59	engineering	engineering	NOUN
american_scientific_journal-5494	41	60	,	,	PUNCT
american_scientific_journal-5494	41	61	technology	technology	NOUN
american_scientific_journal-5494	41	62	,	,	PUNCT
american_scientific_journal-5494	41	63	and	and	CCONJ
american_scientific_journal-5494	41	64	sciences	science	NOUN
american_scientific_journal-5494	41	65	(	(	PUNCT
american_scientific_journal-5494	41	66	asrjets	asrjet	NOUN
american_scientific_journal-5494	41	67	)	)	PUNCT
american_scientific_journal-5494	41	68	(	(	PUNCT
american_scientific_journal-5494	41	69	2019	2019	NUM
american_scientific_journal-5494	41	70	)	)	PUNCT
american_scientific_journal-5494	41	71	volume	volume	NOUN
american_scientific_journal-5494	41	72	62	62	NUM
american_scientific_journal-5494	41	73	,	,	PUNCT
american_scientific_journal-5494	41	74	no	no	DET
american_scientific_journal-5494	41	75	1	1	NUM
american_scientific_journal-5494	41	76	,	,	PUNCT
american_scientific_journal-5494	41	77	pp	pp	ADV
american_scientific_journal-5494	41	78	210	210	NUM
american_scientific_journal-5494	41	79	-	-	SYM
american_scientific_journal-5494	41	80	214	214	NUM
american_scientific_journal-5494	41	81	214	214	NUM
american_scientific_journal-5494	41	82	similarly	similarly	ADV
american_scientific_journal-5494	41	83	if	if	SCONJ
american_scientific_journal-5494	41	84	then	then	ADV
american_scientific_journal-5494	41	85	it	it	PRON
american_scientific_journal-5494	41	86	will	will	AUX
american_scientific_journal-5494	41	87	eigenvalues	eigenvalues	VERB
american_scientific_journal-5494	41	88	for	for	ADP
american_scientific_journal-5494	41	89	n	n	NOUN
american_scientific_journal-5494	41	90	-	-	PUNCT
american_scientific_journal-5494	41	91	d	d	ADV
american_scientific_journal-5494	41	92	fractional	fractional	ADJ
american_scientific_journal-5494	41	93	fourier	fourier	NOUN
american_scientific_journal-5494	41	94	transform	transform	NOUN
american_scientific_journal-5494	41	95	and	and	CCONJ
american_scientific_journal-5494	41	96	for	for	SCONJ
american_scientific_journal-5494	41	97	if	if	SCONJ
american_scientific_journal-5494	41	98	then	then	ADV
american_scientific_journal-5494	41	99	it	it	PRON
american_scientific_journal-5494	41	100	will	will	AUX
american_scientific_journal-5494	41	101	easily	easily	ADV
american_scientific_journal-5494	41	102	obtain	obtain	VERB
american_scientific_journal-5494	41	103	the	the	DET
american_scientific_journal-5494	41	104	same	same	ADJ
american_scientific_journal-5494	41	105	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	41	106	as	as	ADP
american_scientific_journal-5494	41	107	for	for	ADP
american_scientific_journal-5494	41	108	n	n	CCONJ
american_scientific_journal-5494	41	109	-	-	PUNCT
american_scientific_journal-5494	41	110	dimensional	dimensional	ADJ
american_scientific_journal-5494	41	111	fourier	fourier	NOUN
american_scientific_journal-5494	41	112	transform	transform	NOUN
american_scientific_journal-5494	41	113	(	(	PUNCT
american_scientific_journal-5494	41	114	√	√	NUM
american_scientific_journal-5494	41	115	)	)	PUNCT
american_scientific_journal-5494	41	116	(	(	PUNCT
american_scientific_journal-5494	41	117	√	√	NUM
american_scientific_journal-5494	41	118	)	)	PUNCT
american_scientific_journal-5494	41	119	(	(	PUNCT
american_scientific_journal-5494	41	120	√	√	NUM
american_scientific_journal-5494	41	121	)	)	PUNCT
american_scientific_journal-5494	41	122	(	(	PUNCT
american_scientific_journal-5494	41	123	√	√	NUM
american_scientific_journal-5494	41	124	)	)	PUNCT
american_scientific_journal-5494	41	125	3	3	X
american_scientific_journal-5494	41	126	.	.	X
american_scientific_journal-5494	41	127	conclusion	conclusion	NOUN
american_scientific_journal-5494	41	128	we	we	PRON
american_scientific_journal-5494	41	129	have	have	AUX
american_scientific_journal-5494	41	130	eatablished	eatablishe	VERB
american_scientific_journal-5494	41	131	the	the	DET
american_scientific_journal-5494	41	132	mathematical	mathematical	ADJ
american_scientific_journal-5494	41	133	formulation	formulation	NOUN
american_scientific_journal-5494	41	134	of	of	ADP
american_scientific_journal-5494	41	135	n	n	CCONJ
american_scientific_journal-5494	41	136	-	-	PUNCT
american_scientific_journal-5494	41	137	dimesional	dimesional	ADJ
american_scientific_journal-5494	41	138	fractional	fractional	ADJ
american_scientific_journal-5494	41	139	fourier	fourier	NOUN
american_scientific_journal-5494	41	140	transform	transform	NOUN
american_scientific_journal-5494	41	141	in	in	ADP
american_scientific_journal-5494	41	142	very	very	ADV
american_scientific_journal-5494	41	143	easier	easy	ADJ
american_scientific_journal-5494	41	144	manner	manner	NOUN
american_scientific_journal-5494	41	145	and	and	CCONJ
american_scientific_journal-5494	41	146	discuss	discuss	VERB
american_scientific_journal-5494	41	147	their	their	PRON
american_scientific_journal-5494	41	148	eigenvalues	eigenvalue	NOUN
american_scientific_journal-5494	41	149	and	and	CCONJ
american_scientific_journal-5494	41	150	eigen	eigen	PROPN
american_scientific_journal-5494	41	151	functions	function	NOUN
american_scientific_journal-5494	41	152	in	in	ADP
american_scientific_journal-5494	41	153	a	a	DET
american_scientific_journal-5494	41	154	simila	simila	PROPN
american_scientific_journal-5494	41	155	manner	manner	NOUN
american_scientific_journal-5494	41	156	as	as	SCONJ
american_scientific_journal-5494	41	157	for	for	SCONJ
american_scientific_journal-5494	41	158	we	we	PRON
american_scientific_journal-5494	41	159	have	have	VERB
american_scientific_journal-5494	41	160	classical	classical	ADJ
american_scientific_journal-5494	41	161	fourier	fourier	NOUN
american_scientific_journal-5494	41	162	transform	transform	NOUN
american_scientific_journal-5494	41	163	it	it	PRON
american_scientific_journal-5494	41	164	will	will	AUX
american_scientific_journal-5494	41	165	help	help	VERB
american_scientific_journal-5494	41	166	to	to	PART
american_scientific_journal-5494	41	167	apply	apply	VERB
american_scientific_journal-5494	41	168	these	these	DET
american_scientific_journal-5494	41	169	concepet	concepet	NOUN
american_scientific_journal-5494	41	170	in	in	ADP
american_scientific_journal-5494	41	171	more	more	ADJ
american_scientific_journal-5494	41	172	meaning	meaning	NOUN
american_scientific_journal-5494	41	173	full	full	ADJ
american_scientific_journal-5494	41	174	manner	manner	NOUN
american_scientific_journal-5494	41	175	in	in	ADP
american_scientific_journal-5494	41	176	various	various	ADJ
american_scientific_journal-5494	41	177	applications	application	NOUN
american_scientific_journal-5494	41	178	specially	specially	ADV
american_scientific_journal-5494	41	179	in	in	ADP
american_scientific_journal-5494	41	180	case	case	NOUN
american_scientific_journal-5494	41	181	of	of	ADP
american_scientific_journal-5494	41	182	face	face	NOUN
american_scientific_journal-5494	41	183	deduction	deduction	NOUN
american_scientific_journal-5494	41	184	from	from	ADP
american_scientific_journal-5494	41	185	images	image	NOUN
american_scientific_journal-5494	41	186	.	.	PUNCT
american_scientific_journal-5494	42	1	references	reference	NOUN
american_scientific_journal-5494	42	2	[	[	X
american_scientific_journal-5494	42	3	1	1	NUM
american_scientific_journal-5494	42	4	]	]	X
american_scientific_journal-5494	42	5	n.	n.	NOUN
american_scientific_journal-5494	42	6	wiener	wiener	NOUN
american_scientific_journal-5494	42	7	.	.	PUNCT
american_scientific_journal-5494	43	1	hermitian	hermitian	ADJ
american_scientific_journal-5494	43	2	polynomials	polynomial	NOUN
american_scientific_journal-5494	43	3	and	and	CCONJ
american_scientific_journal-5494	43	4	fourier	fouri	ADJ
american_scientific_journal-5494	43	5	analysis	analysis	NOUN
american_scientific_journal-5494	43	6	.	.	PUNCT
american_scientific_journal-5494	44	1	j.	j.	PROPN
american_scientific_journal-5494	44	2	math	math	PROPN
american_scientific_journal-5494	44	3	.	.	PUNCT
american_scientific_journal-5494	45	1	phys	phy	NOUN
american_scientific_journal-5494	45	2	.	.	PUNCT
american_scientific_journal-5494	45	3	,	,	PUNCT
american_scientific_journal-5494	45	4	8:70{73	8:70{73	NUM
american_scientific_journal-5494	45	5	,	,	PUNCT
american_scientific_journal-5494	45	6	1929	1929	NUM
american_scientific_journal-5494	45	7	.	.	PUNCT
american_scientific_journal-5494	46	1	[	[	X
american_scientific_journal-5494	46	2	2	2	X
american_scientific_journal-5494	46	3	]	]	PUNCT
american_scientific_journal-5494	46	4	h.	h.	PROPN
american_scientific_journal-5494	46	5	kober	kober	PROPN
american_scientific_journal-5494	46	6	,	,	PUNCT
american_scientific_journal-5494	46	7	wurzeln	wurzeln	PROPN
american_scientific_journal-5494	46	8	aus	aus	PROPN
american_scientific_journal-5494	46	9	der	der	PROPN
american_scientific_journal-5494	46	10	hankel-	hankel-	PROPN
american_scientific_journal-5494	46	11	,	,	PUNCT
american_scientific_journal-5494	46	12	fourierund	fourierund	PROPN
american_scientific_journal-5494	46	13	aus	aus	PROPN
american_scientific_journal-5494	46	14	anderen	anderen	PROPN
american_scientific_journal-5494	46	15	stetigen	stetigen	PROPN
american_scientific_journal-5494	46	16	transfornationen	transfornationen	PROPN
american_scientific_journal-5494	46	17	,	,	PUNCT
american_scientific_journal-5494	46	18	q.	q.	PROPN
american_scientific_journal-5494	46	19	j	j	PROPN
american_scientific_journal-5494	46	20	math.(oxford	math.(oxford	PROPN
american_scientific_journal-5494	46	21	)	)	PUNCT
american_scientific_journal-5494	46	22	,	,	PUNCT
american_scientific_journal-5494	46	23	10	10	NUM
american_scientific_journal-5494	46	24	,	,	PUNCT
american_scientific_journal-5494	46	25	45–59	45–59	NUM
american_scientific_journal-5494	46	26	(	(	PUNCT
american_scientific_journal-5494	46	27	1939	1939	NUM
american_scientific_journal-5494	46	28	)	)	PUNCT
american_scientific_journal-5494	46	29	.	.	PUNCT
american_scientific_journal-5494	47	1	[	[	X
american_scientific_journal-5494	47	2	3	3	X
american_scientific_journal-5494	47	3	]	]	X
american_scientific_journal-5494	47	4	e.u	e.u	PROPN
american_scientific_journal-5494	47	5	.	.	PUNCT
american_scientific_journal-5494	47	6	condon	condon	PROPN
american_scientific_journal-5494	47	7	.	.	PUNCT
american_scientific_journal-5494	48	1	immersion	immersion	NOUN
american_scientific_journal-5494	48	2	of	of	ADP
american_scientific_journal-5494	48	3	the	the	DET
american_scientific_journal-5494	48	4	fourier	fourier	NOUN
american_scientific_journal-5494	48	5	transform	transform	NOUN
american_scientific_journal-5494	48	6	in	in	ADP
american_scientific_journal-5494	48	7	a	a	DET
american_scientific_journal-5494	48	8	continuous	continuous	ADJ
american_scientific_journal-5494	48	9	group	group	NOUN
american_scientific_journal-5494	48	10	of	of	ADP
american_scientific_journal-5494	48	11	functional	functional	ADJ
american_scientific_journal-5494	48	12	transformations	transformation	NOUN
american_scientific_journal-5494	48	13	.	.	PUNCT
american_scientific_journal-5494	49	1	proc.national	proc.national	ADJ
american_scientific_journal-5494	49	2	academy	academy	NOUN
american_scientific_journal-5494	49	3	sciences	science	NOUN
american_scientific_journal-5494	49	4	,	,	PUNCT
american_scientific_journal-5494	49	5	23:158{164	23:158{164	PROPN
american_scientific_journal-5494	49	6	,	,	PUNCT
american_scientific_journal-5494	49	7	1937	1937	NUM
american_scientific_journal-5494	49	8	.	.	PUNCT
american_scientific_journal-5494	50	1	[	[	X
american_scientific_journal-5494	50	2	4	4	X
american_scientific_journal-5494	50	3	]	]	X
american_scientific_journal-5494	50	4	v.	v.	ADP
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american_scientific_journal-5494	50	6	,	,	PUNCT
american_scientific_journal-5494	50	7	“	"	PUNCT
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american_scientific_journal-5494	50	9	fr	fr	PROPN
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american_scientific_journal-5494	50	13	er	er	INTJ
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american_scientific_journal-5494	50	28	i	i	PRON
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american_scientific_journal-5494	53	1	i	i	PRON
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american_scientific_journal-5494	54	1	,	,	PUNCT
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american_scientific_journal-5494	54	4	,	,	PUNCT
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american_scientific_journal-5494	58	5	-	-	SYM
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american_scientific_journal-5494	59	3	]	]	X
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american_scientific_journal-5494	59	30	,	,	PUNCT
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american_scientific_journal-5494	60	7	,	,	PUNCT
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american_scientific_journal-5494	60	16	.	.	PUNCT
american_scientific_journal-5494	61	1	digital	digital	ADJ
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american_scientific_journal-5494	62	6	,	,	PUNCT
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american_scientific_journal-5494	62	8	,	,	PUNCT
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