2025-L12su10

# 2025-L12su10 - 1 1 ECE2025 Summer 2010 Lecture 12 Digital...

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Unformatted text preview: 1 6/21/2010 1 ECE2025 Summer 2010 Lecture 12 Digital Filtering of Analog Signals (1st pass) Introduction to Z-Transforms 23 Jun 10 6/21/2010 3 ANNOUNCEMENTS Â¡ HW #5 due June 28-29 Â¡ June 23-24 Â¡ Turn in Lab #4 Â¡ Do Lab #5 Â¡ 6/21/2010 4 READING ASSIGNMENTS Â¡ This Lecture: Â¡ Chapter 6, Sections 6-6, 6-7 & 6-8 Â¡ Chapter 7 6/21/2010 5 LECTURE OBJECTIVES Â¡ Two Domains: Time & Frequency Â¡ Track the spectrum of x[n] thru an FIR Filter: Sinusoid-IN gives Sinusoid-OUT Â¡ UNIFICATION : How does Frequency Response affect x(t) to produce y(t) ? D-to-A A-to-D x(t) y(t) y [ n ] x [ n ] ) ( Ë† Ï‰ j e H FIR Ï‰ Ë† Ï‰ Ë† 2 6/21/2010 6 TIME & FREQUENCY FIR DIFFERENCE EQUATION is the TIME-DOMAIN âˆ‘ âˆ‘ = = âˆ’ = âˆ’ = M k M k k k n x k h k n x b n y ] [ ] [ ] [ ] [ âˆ‘ = âˆ’ = M k k j j e k h e H Ë† Ë† ] [ ) ( Ï‰ Ï‰ L + + + + = âˆ’ âˆ’ âˆ’ Ï‰ Ï‰ Ï‰ Ï‰ Ë† 3 Ë† 2 Ë† Ë† ] 3 [ ] 2 [ ] 1 [ ] [ ) ( j j j j e h e h e h h e H 6/21/2010 7 Ex: DELAY by 2 SYSTEM y [ n ] x [ n ] ) ( Ë† Ï‰ j e H y [ n ] x [ n ] ] [ n h ] 2 [ ] [ for ) ( and ] [ Find Ë† âˆ’ = n x n y e H n h j Ï‰ ] 2 [ ] [ âˆ’ = n n h Î´ } 1 , , { = k b Ï‰ Ë† Ï‰ Ë† 6/21/2010 8 DELAY by 2 SYSTEM k = 2 ONLY y [ n ] x [ n ] ] 2 [ âˆ’ n Î´ ] 2 [ ] [ for ) ( and ] [ Find Ë† âˆ’ = n x n y e H n h j Ï‰ âˆ‘ = âˆ’ âˆ’ = M k k j j e k e H Ë† Ë† ] 2 [ ) ( Ï‰ Ï‰ Î´ ) ( Ë† Ï‰ j e H y [ n ] x [ n ] Ï‰ Ë† 2 j e âˆ’ Ï‰ Ë† Ï‰ Ë† 6/21/2010 9 GENERAL DELAY PROPERTY ONLY ONE non-ZERO TERM for k at k = n d d n j M k k j d j e e n k e H Ï‰ Ï‰ Ï‰ Î´ Ë† Ë† Ë† ] [ ) ( âˆ’ = âˆ’ = âˆ’ = âˆ‘ ] [ ] [ for ) ( and ] [ Find Ë† d j n n x n y e H n h âˆ’ = Ï‰ ] [ ] [ d n n n h âˆ’ = Î´ 3 6/21/2010...
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2025-L12su10 - 1 1 ECE2025 Summer 2010 Lecture 12 Digital...

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