A Residue Number System for Wideband Acousto-Optic Spectrum Analysis

Abstract

A b s t r a c t An a r c h i t e c t u r e i s p r e s e n t e d which p e r f o r m s e x t r e m e l y wideband a c o u s t o -o p t i c (AO) s p e c t r u m a n a l y s i s u s i n g r f -p r e p r o c e s s i n g a n d smart, r a p i d p o s t p r o c e s s i n g c i r c u i t r y based on r e s i d u e number t h e o r y . For k c h a n n e l s e a c h w i t h % r e s o l u t i o n e l e m e n t s , where t h e % ' s are r e l a t i v e l y p r i m e , t h e t o t a l number of p o s s i b l e r e s o l u t i o n e l e m e n t s i s g i v e n by IIm . The t o t a l r f bandwidth is f o l d e d i n t o nk b a n i s e a c h % e l e m e n t s wide, and o u t p u t sof t h e k c h a n n e l s from t h e s p e c t r u m a n a l y z e r a r e compared t o d e t e r m i n e t h e f r e q u e n c y and i n t e n s i t y of s i g n a l s w i t h i n t h e s y s t e m a p e r t u r e . C u r r e n t h a r d w a r e performs A0 s p e c t r u m a n a l y s i s o v e r a 50-MHz bandwidth w i t h 25 kHz r e s o l u t i o n . b b d i f ic a t i o n s t o t h i s hardware e x t e n d s t h e bandwidth t o a p r a c t i c a l l i m i t of a p p r o x i m a t e l y 300 MHz, m a i n t a i n i n g t h e 25-kHz s y s t e m r e s o l u t i o n . O t h e r s y s t e m s a r e p r o p o s e d f o r w i d e r b a n d w i d t h s , a n d t h e p o t e n t i a l performance p a r a m e t e r s f o r t h e s e s y s t e m s a r e examined. The p e r f o r m a n c e depends p r i m a r i l y on t h e c h o i c e of moduli T, t h e number of moduli k , and t h e number of bands nk. 1. I n t r o d u c t i o n T h i s p a p e r d e s c r i b e s a n a r c h i t e c t u r e which p e r f o r m s e x t r e m e l y wideband a c o u s t o a p t i c (AO) s p e c t r u m a n a l y s i s u s i n g residue-number-theory b a s e d r f -p r e p r o c e s s i n g a n d smart, r a p i d p o s t p r o c e s s i n g c i r c u i t r y . The a r c h i t e c t u r e i s a m o d i f i c a t i o n of e x i s t i n g A 0 p r o c e s s o r s [ 1 , 2 ] , i n which i t i s p o s s i b l e t o p e r f o r m A0 s p e c t r u m a n a l y s i s o v e r a 51.2-MHz bandwidth w i t h 25-KHz r e s o l u t i o n by u s i n g two 30-MHz bandwidth Bragg c e l l s , e a c h c e l l h a v i n g a 45-MHz c e n t e r f r e q u e n c y . T h i s i s a two-channel s y s t e m , where e a c h c h a n n e l h a s 1024 r e s o l u t i o n e l e m e n t s i n t h e p h o t o d i o d e d e t e c t o r a r r a y . In a c o n v e n t i o n a l s p e c t r u m a n a l y z e r w i t h k c h a n n e l s , e a c h w i t h m r e s o l u t i o n e l e m e n t s , t h e t o t a l number of p o s s i b l e r e s o l u t i o n e l e m e n t s i s g i v e n by k x m, a n d t h e t o t a l bandwidth i s g i v e n by BW = k x m x r , where r i s t h e r e s o l u t i o n . I n t h e p r o p o s e d a r c h i t e c t u r e , c o n s i s t i n g of k c h a n n e l s ( k , , k 2 ,..., k), w i t h m l , m2 ,..., % r e s o l u t i o n e l e m e n t s , r e s p e c t i v e l y , t h e t o t a l p o s s ...