D:\sbornik\...\Gen_Haar_Tr2.DVI Mathematical Problems of Computer Science 31, 79{89, 2008. Fast Gener alized H aar T r ansfor ms H a ko b G. S a r u kh a n ya n Institue for Informatics and Automation Problems of NAS of RA e-mail: hakop@ipia.sci.am Abstract The fast generalized Haar transform algorithms of orders 4n; 3n; and 5n are pre- sented. Refer ences [1 ] A h m e d N ., R a o K .R . Or t h o g o n a l Tr a n s fo r m s fo r D ig it a l S ig n a l P r o c e s s in g . S p r in g e r - V e r la g , N e w Y o r k, 1 9 7 5 . [2 ] H a a r Z. Zu r Th e o r ie d e r o r t h o g o n a le n fu n kt io n e n s ys t e m e , Ma t h . A n n ., vo l 6 9 , p .3 3 1 - 3 7 1 , 1 9 1 4 . [3 ] R a o K .R ., N a r a s im h a m , R e vu lu r i K . A Fa m ily o f d is c r e t e H a a r t r a n s fo r m s , Co m p u t . E le c t r . E n g r g ., vo l. 2 , p .3 6 7 -3 6 8 , 1 9 7 5 . [4 ] S e b e r r y J., Zh a n g X .M. S o m e o r t h o g o n a l d e s ig n s a n d c o m p le x H a d a m a r d m a t r ic e s b y u s in g t wo H a d a m a r d m a t r ic e s . A u s t r a l. J. o f Co m b in . Th e o r y., N o .4 , p .9 3 -1 0 2 , 1 9 9 1 . [5 ] Co r in t h io s M.J. A n e w c la s s o f g e n e r a l-b a s e m a t r ic e s a n d a fo r m a lis m fo r o p t im a l p a r a l- le l/ p ip e lin e d c o m p u t e r a r c h it e c t u r e . E le c t r ic a l a n d Co m p u t e r E n g in e e r in g , 1 9 9 3 . Ca n a - d ia n Co n fe r e n c e o n 1 4 -1 7 S e p t ., vo l.2 , p .8 5 1 -8 5 6 , 1 9 9 3 . [6 ] Min g yo n g Zh o u , Zh o n g ka n L iu , H a m a H . A r e s o lu t io n -c o n t r o lla b le h a r m o n ic a l r e t r ie va l a p p r o a c h o n t h e Ch r e s t e n s o n d is c r e t e s p a c e . IE E E Tr a n s a c t io n s , S ig n a l P r o c e s s in g , vo l.4 2 , Is s u e 5 , p .1 2 8 1 -1 2 8 4 , 1 9 9 4 . [7 ] Mo r a g a , C., P o s wig J. P r o p e r t ie s o f t h e Zh a n g -H a r t le y s p e c t r u m o f p a t t e r n s . P r o c e e d - in g s o f t h e Twe n t ie t h In t e r n a t io n a l S ym p o s iu m , Mu lt ip le -V a lu e d L o g ic , p .6 2 -6 8 , 1 9 9 0 . [8 ] A g a ia n S ., B a ja d ia n H . Ge n e r a liz e d o r t h o g o n a l H a a r s ys t e m s : S yn t h e s is , Me t r ic a n d Co m p u t in g P r o p e r t ie s . H a a r Me m o r ia l Co n fe r e n c e , vo l.1 , p .9 7 -1 1 3 , Co llo g . Ma t h . S o c . Ja n o s B o lya i, 4 9 , N o r t h -H o lla n d , A m s t e r d a m , N e w Y o r k, 1 9 8 7 . [9 ] Ma lla t S . A W a ve le t To u r o f S ig n a l P r o c e s s in g . A c a d e m ic P r e s s , 2 0 0 1 . г³ñÇ ÁݹѳÝñ³óí³Í ³ñ³· Ó¨³÷áËáõÃÛáõÝÝ»ñ Ð. ê³ñáõ˳ÝÛ³Ý ²Ù÷á÷áõÙ Ðá¹í³ÍáõÙ Ý»ñϳ۳óí³Í »Ý 4 n; 3 n; ¨ 5 n ϳñ·Ç г³ñÇ ÁݹѳÝñ³óí³Í ³ñ³· Ó¨³÷áËáõÃÛáõÝÝ»ñÇ ³É·áñÇÃÙÝ»ñÁ: 7 9