slaa228 digital fir filter design using the msp430f16x

7/24/2019 slaa228 Digital FIR Filter Design Using the MSP430F16x

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A p p l i c a t i o n R e p o r t S L A A 2 2 8 N o v e m b e r 2 0 0 4

D i g i t a l F I R F i l t e r D e s i g n U s i n g t h e M S P 4 3 0 F 1 6 x M u r u g a v e l R a j u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M S P 4 3 0

A B S T R A C T

T h i s a p p l i c a t i o n r e p o r t d e s c r i b e s a n F I R f i l t e r i m p l e m e n t a t i o n u s i n g t h e M S P 4 3 0 F 1 6 x a n d t h e M S P 4 3 0 F 1 6 1 x f a m i l y d e v i c e s . T h e c o m p l e t e f i l t e r a l g o r i t h m i s e x e c u t e d b y t h e 3 - c h a n n e l D M A p e r i p h e r a l a n d t h e h a r d w a r e m u l t i p l i e r p e r i p h e r a l . T h e s e m o d u l e s a r e u s e d i n c o n j u n c t i o n w i t h t h e a l l o c a t e d c o e f f i c i e n t t a b l e i n t h e p r o g r a m m e m o r y a n d t h e c i r c u l a r d a t a b u f f e r s p a c e d e d i c a t e d i n t h e R A M o f t h e d e v i c e . T h e h a r d w a r e m u l t i p l i e r p e r f o r m s t h e s i g n e d m u l t i p l y - a n d - a c c u m u l a t e ( M A C S ) o p e r a t i o n s i n t h e a l g o r i t h m . T h e i n t e g r a t e d a n a l o g - t o - d i g i t a l c o n v e r t e r , A D C 1 2 , i s u s e d f o r d a t a a c q u i s i t i o n . T h e

s o f t w a r e f o r t h e f i l t e r i s w r i t t e n i n s u c h a w a y t h a t a l l t h e f i l t e r p a r a m e t e r s i n c l u d i n g t h e c o e f f i c i e n t s a r e l o a d e d i n t o a l o o k - u p t a b l e . T h i s a l l o w s t h e s a m e f i l t e r p r o g r a m t o b e u s e d f o r a n y t y p e o f F I R f i l t e r i m p l e m e n t a t i o n s u c h a s h i g h - p a s s , l o w - p a s s , b a n d - p a s s a n d b a n d - r e j e c t f i l t e r s . T h e i n t e g r a t e d d i g i t a l - t o - a n a l o g c o n v e r t e r , D A C 1 2 , c a n b e u s e d f o r c o n v e r t i n g t h e f i l t e r o u t p u t b a c k i n t o t h e a n a l o g d o m a i n i f r e q u i r e d .

D i g i t a l f i n i t e i m p u l s e r e s p o n s e ( F I R ) f i l t e r s f o r m t h e b a s i s f o r n u m e r o u s d i g i t a l s i g n a l p r o c e s s i n g a p p l i c a t i o n s . T h e b a s i c o p e r a t i o n n e e d e d t o i m p l e m e n t a F I R f i l t e r i s t h e s i g n e d m u l t i p l y - a n d - a c c u m u l a t e ( M A C S ) , w h i c h i s t r a d i t i o n a l l y p e r f o r m e d u s i n g a h a r d w a r e m u l t i p l i e r p e r i p h e r a l i n a n y D S P d e v i c e . S o m e

o f t h e M S P 4 3 0 d e v i c e s h a v e a n i n t e g r a t e d h a r d w a r e m u l t i p l i e r t h a t c a n p e r f o r m t h i s M A C S o p e r a t i o n a l l o w i n g t h e s e d e v i c e s t o r u n t h e F I R f i l t e r a l g o r i t h m m o r e e f f i c i e n t l y t h a n d e v i c e s w i t h o u t a b u i l t - i n h a r d w a r e m u l t i p l i e r .

E q u a t i o n 1 s h o w s a m a t h e m a t i c a l e x p r e s s i o n f o r t h e F I R f i l t e r ,

w h e r e k i s t h e t i m e s t e p , y ( k ) i s t h e f i l t e r o u t p u t a t t i m e k , x ( k i ) i s t h e s a m p l e d i n p u t a t t i m e k i , a i i s t h e f i l t e r c o e f f i c i e n t i , a n d N i s t h e o r d e r o f t h e f i l t e r ( = n u m b e r o f t a p s 1 ) .

I n a d d i t i o n t o t h e M A C S o p e r a t i o n t h e p r o c e s s o r h a n d l e s t h e t a s k o f m o v i n g t h e d i g i t a l s a m p l e s a n d f i l t e r c o e f f i c i e n t s f r o m m e m o r y t o t h e M A C h a r d w a r e , r e t r i e v i n g t h e r e s u l t s a n d s t o r i n g t h e m i n t o m e m o r y . I n a r e a l - t i m e d i g i t a l f i l t e r a l g o r i t h m , t h e c o m p u t a t i o n a n d m e m o r y - m o v e o p e r a t i o n s h a v e t o b e c o m p l e t e d

w i t h i n o n e s a m p l e p e r i o d . T h e n u m b e r o f c o m p u t a t i o n s t o b e p e r f o r m e d w i t h i n o n e s a m p l e p e r i o d d e p e n d s o n t h e n u m b e r o f t a p s o f t h e f i l t e r , i . e , t h e o r d e r o f t h e f i l t e r . T h e o r d e r o f t h e f i l t e r i s d e t e r m i n e d b y t h e r e q u i r e d f i l t e r p e r f o r m a n c e c h a r a c t e r i s t i c s . W h e n h i g h e r o r d e r f i l t e r s a r e c o m b i n e d w i t h f a s t e r s a m p l i n g r a t e s , t h e d e m a n d o n t h e p r o c e s s o r b e c o m e s v e r y h i g h . T h i s l i m i t s t y p i c a l M C U s t o h a n d l e a r e a l - t i m e F I R f i l t e r a l g o r i t h m o n l y a t l o w s a m p l e r a t e s a n d w i t h a r e d u c e d n u m b e r o f f i l t e r t a p s .

T h e M S P 4 3 0 F 1 6 9 w i t h i t s r i c h p e r i p h e r a l s e t h a n d l e s t h e F I R f i l t e r a l g o r i t h m i n a d i f f e r e n t m a n n e r c o m p a r e d t o c o n v e n t i o n a l M C U s . T h i s d e v i c e h a s a t h r e e c h a n n e l D M A p e r i p h e r a l t h a t h a n d l e s t h e r e q u i r e d d a t a , c o e f f i c i e n t a n d r e s u l t m o v e m e n t b e t w e e n t h e m e m o r y a n d t h e M A C , d r a m a t i c a l l y i m p r o v i n g t h e c o m p u t a t i o n e f f i c i e n c y o f t h e r e a l - t i m e F I R f i l t e r a l g o r i t h m r u n n i n g o n - c h i p .

D i g i t a l F I R F i l t e r D e s i g n U s i n g t h e M S P 4 3 0 F 1 6 x S L A A 2 2 8 N o v e m b e r 2 0 0 4 1


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Timer_A

TACCR2

MCLK

HardwareMultiplier

MACS

OP2

RESHIRESLO

DMA

DMAChannel0

DMA

Channel1

DMAChannel2

CoefficientTable

FIR FilterOutput Data

a0/ak

a1/ak1

an/akn

UpperandLower

CircularBuffer

Samples

2 F I R F i l t e r S o f t w a r e A l g o r i t h m

F I R F i l t e r S o f t w a r e A l g o r i t h m

T h e D M A p e r i p h e r a l c o m p l e t e s a m e m o r y t r a n s f e r o p e r a t i o n i n t w o C P U c l o c k c y c l e s . A d d i t i o n a l l y i t h a s s o f t w a r e - s e l e c t a b l e t r i g g e r s o u r c e s t h a t m a k e i t i d e a l l y s u i t a b l e f o r t h e F I R f i l t e r i m p l e m e n t a t i o n . T h e F I R f i l t e r r u n s o n t h e D M A - M A C S - M e m o r y c o m b i n a t i o n a u t o n o m o u s l y w i t h o u t t h e i n t e r v e n t i o n o f t h e C P U . T h e C P U i s p r i m a r i l y o n l y b e i n g u s e d f o r t h e i n i t i a l i z a t i o n o f p e r i p h e r a l s .

T h e c o e f f i c i e n t s o f t h e F I R f i l t e r a r e s y m m e t r i c a l i n n a t u r e . D u e t o t h i s t h e c o e f f i c i e n t t a b l e s i z e c a n b e r e d u c e d t o h a l f t h e n u m b e r o f t a p s o f t h e f i l t e r . I n a D S P d e v i c e t h e i n p u t s a m p l e d a t a i s s t o r e d i n a

c i r c u l a r b u f f e r t o i m p l e m e n t t h e m o v e m e n t o f t h e s a m p l e s t h r o u g h t h e F I R c o m p u t a t i o n b l o c k s w i t h o u t h a v i n g t o l i t e r a l l y m o v e t h e d a t a i n m e m o r y . W h e n a n e w s a m p l e i s a d d e d t o t h e b u f f e r , i t a u t o m a t i c a l l y r e p l a c e s t h e o l d e s t o n e . A s i m i l a r c i r c u l a r b u f f e r a r r a n g e m e n t i s m a d e i n t h e l i n e a r m e m o r y s p a c e o f t h e M S P 4 3 0 b y a f o l d e d a d d r e s s s t r u c t u r e a p p r o a c h u s i n g D M A c h a n n e l s 1 a n d 2 . F i g u r e 1 r e p r e s e n t s t h e b l o c k d i a g r a m o f t h e F I R f i l t e r i m p l e m e n t a t i o n i n t h e M S P 4 3 0 F 1 6 9 .

F i g u r e 1 . F I R I m p l e m e n t a t i o n U s i n g t h e M S P 4 3 0 F 1 6 9

T h e F I R f i l t e r s o f t w a r e f o r t h e M S P 4 3 0 F 1 6 9 i s w r i t t e n i n a s s e m b l y l a n g u a g e t o a c h i e v e m a x i m u m p e r f o r m a n c e . T h e s o f t w a r e i s w r i t t e n t o a c c e p t t h e c o e f f i c i e n t s s t o r e d i n t h e f o r m o f a l o o k - u p t a b l e p o i n t e d t o b y t h e l a b e l F I L T E R i n p r o g r a m m e m o r y . T h e f i r s t v a l u e i n t h e l o o k - u p t a b l e i s t h e v a l u e f o r T i m e r _ A f o r t h e r e q u i r e d s a m p l i n g f r e q u e n c y . T h e n e x t v a l u e i s t h e n u m b e r o f f i l t e r t a p s N a n d t h e r e m a i n i n g v a l u e s a r e f i l t e r c o e f f i c i e n t s .

D i g i t a l F I R F i l t e r D e s i g n U s i n g t h e M S P 4 3 0 F 1 6 x 2 S L A A 2 2 8 N o v e m b e r 2 0 0 4


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4 C a l c u l a t i n g t h e F I R F i l t e r C o e f f i c i e n t s

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T h e d e p t h o f t h e R A M b u f f e r i s 2 x t h e n u m b e r o f t a p s t o m i n i m i z e t h e c i r c u l a r b u f f e r o v e r h e a d . I n t h i s i m p l e m e n t a t i o n n o a d d i t i o n a l i n p u t o r o u t p u t b u f f e r s t o t h e f i l t e r s t r u c t u r e a r e p r o v i d e d . T h e s e c a n b e a d d e d t o m i n i m i z e o r e l i m i n a t e t h e e f f e c t o f i n t e r r u p t l a t e n c y .

T h e D M A i s c o n f i g u r e d a s f o l l o w s :

D M A 0 : L o a d s t h e f i l t e r c o e f f i c i e n t s f r o m t h e l o o k - u p t a b l e t o t h e h a r d w a r e m u l t i p l i e r s i g n e d m u l t i p l y a n d a c c u m u l a t e ( M A C S ) r e g i s t e r

D M A 1 : S e n d s s a m p l e d a t a t o M A C a n d m o v e s t h e u p - d i r e c t i o n s a m p l e p o i n t e r o f t h e c i r c u l a r b u f f e r

D M A 2 : S e n d s s a m p l e d a t a t o M A C a n d m o v e s t h e d o w n - d i r e c t i o n s a m p l e p o i n t e r o f t h e c i r c u l a r b u f f e r

T h e t h r e e D M A c h a n n e l s a r e e n a b l e d a n d d i s a b l e d t o g e t h e r b y m o d u l a t i n g t h e T A C C R 0 r e g i s t e r v a l u e b e t w e e n 0 x 0 0 ( d i s a b l e d ) a n d 0 x 0 B ( t r i g g e r s e v e r y 1 2 c l o c k s ) .

T h e c o m p u t a t i o n t a k e s a d v a n t a g e o f t h e s y m m e t r i c a l n a t u r e o f t h e F I R f i l t e r s t r u c t u r e a s m e n t i o n e d i n t h e e a r l i e r s e c t i o n s . T h i s a l g o r i t h m l o a d s t h e f i r s t c o e f f i c i e n t v a l u e t o t h e M A C S r e g i s t e r v i a D M A 0 a n d t h e n m o v e s t w o s a m p l e s s e q u e n t i a l l y t o t h e O P 2 r e g i s t e r o f t h e h a r d w a r e m u l t i p l i e r . T h e f i r s t s a m p l e i s l o a d e d b y D M A 1 a n d t h e s e c o n d s a m p l e b y D M A 2 . D M A 1 s c a n s t h r o u g h t h e u p p e r h a l f o f t h e s a m p l e s w i n d o w b y i n c r e m e n t i n g t h e s o u r c e a d d r e s s a f t e r e v e r y t r a n s f e r a n d D M A 2 s c a n s t h r o u g h t h e l o w e r h a l f o f t h e s a m p l e s w i n d o w b y d e c r e m e n t i n g t h e s o u r c e a d d r e s s a f t e r e v e r y t r a n s f e r .

D u e t o t h e s y m m e t r y o f t h e c o e f f i c i e n t v a l u e s o n l y h a l f o f t h e c o e f f i c i e n t s a r e s t o r e d i n t h e l o o k - u p t a b l e . I f t h e n u m b e r o f t a p s , N , i s e v e n t h e f i r s t h a l f i s s t o r e d . I f N i s o d d , t h e n t h e n u m b e r o f c o e f f i c i e n t s s t o r e d i s ( N + 1 ) / 2 w i t h t h e l a s t c o e f f i c i e n t v a l u e d i v i d e d b y t w o .

T h e a s s e m b l y s o u r c e c o d e f o r t h i s a l g o r i t h m i s i n c l u d e d i n t h e d e m o c o d e p r o v i d e d a s a . z i p f i l e a l o n g w i t h t h i s a p p l i c a t i o n r e p o r t . T h e s o u r c e c o d e c a n b e t a i l o r e d t o s p e c i f i c n e e d s o f a n a p p l i c a t i o n a s r e q u i r e d .

T h e d e m o s o f t w a r e i n c l u d e d w i t h t h i s a p p l i c a t i o n r e p o r t u t i l i z e s t h e a l g o r i t h m d e s c r i b e d a b o v e . T h e i n p u t s a m p l e s a r e p r o v i d e d d i r e c t l y t o t h e f i l t e r i n p u t a n d t o t h e i n t e g r a t e d d i g i t a l - t o - a n a l o g c o n v e r t e r , D A C 0 , b y a s w e e p f r e q u e n c y g e n e r a t e d u s i n g t h e 1 2 - b i t l o o k u p t a b l e v a l u e s f r o m t h e a t t a c h e d s i n e w a v e d a t a f i l e : s i n e 8 1 9 2 _ 1 2 b . d a t . T h e f i l t e r p a r a m e t e r s a r e s t o r e d i n t h e p r o g r a m m e m o r y p o i n t e d b y t h e l a b e l F i l t e r . T h r e e e x a m p l e s a r e s h o w n : a 4 0 - t a p l o w - p a s s f i l t e r , a 2 2 4 - t a p b a n d - p a s s f i l t e r a n d a 1 0 1 - t a p b a n d - s t o p

f i l t e r . T h e f i l t e r o u t p u t i s s e n t t o D A C 1 a n d c a n b e c o n n e c t e d t o a n o s c i l l o s c o p e f o r v i e w i n g o f t h e f i l t e r o u t p u t r e s p o n s e . T h e c o r r e s p o n d i n g i n p u t w a v e f o r m c a n b e s e e n a t t h e D A C 0 o u t p u t u s i n g a n o t h e r c h a n n e l o f t h e o s c i l l o s c o p e . W h e n t h e p r o g r a m i s d o w n l o a d e d t o t h e d e v i c e a n d e x e c u t e d t h e i n p u t f r e q u e n c y s w e e p s t h r o u g h t h e s e t r a n g e . T h e o u t p u t r e s p o n s e c a n b e s e e n o n t h e c h a n n e l c o n n e c t e d t o D A C 1 o u t p u t . T h e a p p r o p r i a t e f i l t e r f o r e x e c u t i o n i s s e l e c t e d b y c o m m e n t i n g o u t t h e u n w a n t e d f i l t e r t a b l e l a b e l s .

T h e d e m o s o f t w a r e c a n b e r u n o n a F E T 1 4 0 w i t h a M S P 4 3 0 F 1 6 9 p o p u l a t e d i n t h e s o c k e t . N o t e t h a t t h e F E T t a r g e t b o a r d d o e s n o t h a v e a n 8 M H z h i g h f r e q u e n c y c r y s t a l o r r e s o n a t o r c o n n e c t e d t o i t a n d m u s t b e p o p u l a t e d f o r t h i s d e m o s o f t w a r e t o f u n c t i o n a s i s . T h e s o f t w a r e p r o v i d e d w i t h t h i s r e p o r t i s f o r I A R e m b e d d e d w o r k b e n c h K i c k s t a r t v e r s i o n w h i c h c a n b e d o w n l o a d e d f o r f r e e f r o m t h e M S P 4 3 0 w e b p a g e .

T h e f i l t e r c o e f f i c i e n t s a n d t h e o r d e r o f t h e f i l t e r a r e c a l c u l a t e d a s p e r t h e r e q u i r e m e n t s o f t h e f i l t e r t y p e a n d p a r a m e t e r s . T h i s a p p l i c a t i o n u s e s a v e r y i n e x p e n s i v e p r o g r a m c a l l e d S c o p e F I R f r o m w w w . i o w e g i a n . c o m . N o t o n l y d o e s t h i s p r o g r a m c a l c u l a t e t h e f i l t e r c o e f f i c i e n t s b u t a l s o s i m u l a t e s t h e f i l t e r r e s p o n s e s f o r a l l t y p e s o f F I R f i l t e r s . T h e c a l c u l a t e d c o e f f i c i e n t s c a n b e c o n v e r t e d t o s i g n e d f r a c t i o n h e x f o r m a t b y c h a n g i n g t h e d a t a f o r m a t a n d c a n b e i m p o r t e d a s t e x t o r e a s i l y c o p i e d a n d p a s t e d i n t o t h e a s s e m b l e r s o u r c e c o d e .

T h e t h r e e c h a n n e l D M A p e r i p h e r a l w i t h v a r i o u s t r i g g e r s a n d t h e h a r d w a r e m u l t i p l i e r a l l o w s r e a l i z a t i o n o f v e r y e f f i c i e n t F I R f i l t e r a l g o r i t h m s u s i n g t h e M S P 4 3 0 F 1 6 9 . A c h i e v i n g a h i g h e r n u m b e r o f t a p s w i t h f a s t e r s a m p l i n g r a t e i s m a d e p o s s i b l e w i t h t h i s i m p l e m e n t a t i o n u n l i k e u s i n g c o n v e n t i o n a l M C U s t h a t d o n o t h a v e a h a r d w a r e m u l t i p l i e r t o p e r f o r m M A C S a n d t h e m u l t i - c h a n n e l D M A t o e x e c u t e t h e f i l t e r a l g o r i t h m .

D i g i t a l F I R F i l t e r D e s i g n U s i n g t h e M S P 4 3 0 F 1 6 x S L A A 2 2 8 N o v e m b e r 2 0 0 4 3


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www.ti.com

6 R e f e r e n c e s

R e f e r e n c e s

T a b l e 1 s h o w s t h e p e r f o r m a n c e t h a t c a n b e a c h i e v e d u s i n g t h e M S P 4 3 0 F 1 6 9 w i t h a n 8 M H z C P U c l o c k f r e q u e n c y w i t h r e s p e c t t o f i l t e r t a p s a n d t h e m a x i m u m s a m p l i n g r a t e p o s s i b l e w i t h 1 0 0 % C P U l o a d i n g .

T a b l e 1 . M S P 4 3 0 F 1 6 9 F I R F i l t e r B e n c h m a r k s

N u m b e r o f T a p s , M a x i m u m S a m p l i n g R a t e ( k H z ) N u m b e r o f C P U C l o c k s

N ( 1 0 0 % C P U l o a d i n g )

3 2 3 1 0 2 5

5 0 4 1 0 1 9

1 0 0 7 3 0 1 1

P r a c t i c a l s i g n a l p r o c e s s i n g n e e d s a r e t y p i c a l l y m u c h l o w e r t h a n t h e m a x i m u m p o s s i b l e n u m b e r s s h o w n i n t h e t a b l e . I n s u c h c a s e s m o r e f r e e C P U r e s o u r c e s w i l l b e a v a i l a b l e f o r t h e u s e r a p p l i c a t i o n w h i l e r u n n i n g t h e F I R f i l t e r

1 . U n d e r s t a n d i n g D i g i t a l S i g n a l P r o c e s s i n g b y R i c h a r d G . L y o n s

2 . T h e S c i e n t i s t a n d E n g i n e e r s G u i d e t o D i g i t a l S i g n a l P r o c e s s i n g b y S t e v e n W . S m i t h 3 . M S P 4 3 0 x 1 x x F a m i l y U s e r s G u i d e ( S L A U 0 4 9 )

4 . M S P 4 3 0 x 1 6 x D a t a s h e e t ( S L A S 3 6 8 )

D i g i t a l F I R F i l t e r D e s i g n U s i n g t h e M S P 4 3 0 F 1 6 x 4 S L A A 2 2 8 N o v e m b e r 2 0 0 4
http://www-s.ti.com/sc/techlit/SLAS368http://www-s.ti.com/sc/techlit/SLAU049


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slaa228 digital fir filter design using the msp430f16x

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