8.SecondOrderFiltersx4

# 8.SecondOrderFiltersx4 - M o t i v a t i o n Y s = ∑ M k...

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Unformatted text preview: M o t i v a t i o n Y ( s ) = ∑ M k = b k s k ∑ N k = a k s k ! X ( s ) = H ( s ) X ( s ) • S e c o n d o r d e r fi l t e r s a r e fi l t e r s w i t h a d e n o m i n a t o r p o l y n o m i a l t h a t i s o f s e c o n d o r d e r • U s u a l l y t h e r o o t s ( p o l e s ) a r e c o m p l e x p 1 , 2 = − ζ ω n ± j ω n p 1 − ζ 2 • I n m a n y a p p l i c a t i o n s , s e c o n d o r d e r fi l t e r s m a y b e s u ﬃ c i e n t • A r e a l s o t h e b u i l d i n g b l o c k s f o r h i g h e r- o r d e r fi l t e r s J . M c N a m e s P o r t l a n d S t a t e U n i v e r s i t y E C E 2 2 2 S e c o n d O r d e r F i l t e r s V e r . 1 . 2 3 S e c o n d O r d e r F i l t e r s O v e r v i e w • W h a t ’ s d i ff e r e n t a b o u t s e c o n d o r d e r fi l t e r s • R e s o n a n c e • S t a n d a r d f o r m s • F r e q u e n c y r e s p o n s e a n d B o d e p l o t s • S a l l e n- K e y fi l t e r s J . M c N a m e s P o r t l a n d S t a t e U n i v e r s i t y E C E 2 2 2 S e c o n d O r d e r F i l t e r s V e r . 1 . 2 1 S t a n d a r d F o r m H ( s ) = N ( s ) s 2 ω 2 n + s Q ω n + 1 • S e c o n d o r d e r fi l t e r s c a n b e d e s i g n e d a s l o w p a s s , h i g h p a s s , b a n d p a s s , o r n o t c h fi l t e r s • A l l f o u r t y p e s c a n b e e x p r e s s e d i n s t a n d a r d f o r m s h o w n a b o v e • N ( s ) i s a p o l y n o m i a...
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## This note was uploaded on 10/02/2011 for the course ECON 223 taught by Professor Conner during the Winter '11 term at Portland State.

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8.SecondOrderFiltersx4 - M o t i v a t i o n Y s = ∑ M k...

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