D:\sbornik\...\FIR_IIAP.DVI


Mathematical Problems of Computer Science 23, 2004, 54{58.

On Compensation of Discr ete Four ier T r ansfor m E r r or

D a vid G. A s a t r ya n

Institute for Informatics and Automation Problems of NAS of RA

e-mail dasat@ipia.sci.am

Abstract

A problem of reduction of the percentage (relative) error, appearing at a ¯nite
signal spectrum restoration by means of Discrete Fourier Transform is considered. A
method based on using of a ¯nite impulse ¯lter with various impulse responses is
o®ered. Depending on errors of the initial spectrum, a percentage error expression
derivable after using the ¯ltering is obtained. A criterion for comparison between
speci¯ed errors at a large number of discrete points is o®ered. Conditions, when the
¯lter of given response reduces the restoration error module, are obtained. Examples
with uniform window and some ¯nite functions of standard type are considered.

Keywords - FFT, discretization error, spectrum, spectrum restoration, ¯nite im-
pulse ¯lter, error compensation

Refer ences

[1 ] L . R . R a b in e r a n d B . Go ld , Th e o r y a n d A p p lic a t io n o f D ig it a l S ig n a l P r o c e s s in g ,
P r e n t ic e -H a ll, In c ., N e w Je r s e y, 1 9 7 5 .

[2 ] D . S la t e r , N e a r -Fie ld A n t e n n a Me a s u r e m e n t s , A r t e c h H o u s e , 1 9 9 1 .

[3 ] W .K . P r a t t , D ig it a l Im a g e P r o c e s s in g , N e w Y o r k, W ile y, 1 9 9 1 .

[4 ] D .G. A s a t r ya n , " D is c r e t iz a t io n E r r o r o f Im a g e S p e c t r u m R e s t o r a t io n " , P r o c . o f 3 r d
In t e r n a t io n a l S ym p o s iu m o n Im a g e a n d S ig n a l P r o c e s s in g a n d A n a lys is ( IS P A 2 0 0 3 ) ,
R o m e , It a ly, 2 0 0 3 , V .2 , p p . 8 2 6 -8 2 8 .

[5 ] D .G. A s a t r ya n a n d L .A . Ta d e vo s ya n , " On E r r o r o f A p p r o xim a t e Ca lc u la t io n o f t h e Fi-
n it e Fu n c t io n Fo u r ie r Tr a n s fo r m " . R a d io t e c h n ika ( R a d io t e c h n ic s , Mo s c o w, in R u s s ia n ) ,
N 1 0 , 1 9 8 8 , p p 3 3 -3 4 .

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D. G. Asatryan 5 5

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