2025-L24 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW Quiz...

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ECE-2025 Spring-2004 Lecture 24 H(z) & Frequency Response for IIR Systems 16-April-04 4/14/2004 ECE-2025 Spring-04 jMc 2 Info: Web-CT, Lab, HW ± Quiz #3: Results ± Median = 70 ± Quiz #3: Resolve any grade changes by Friday (23-April) ± Total Points posted: ± Max = 70; ± percentage is a projection ± 8 Labs, 10 HWs included so far ± No drops 4/14/2004 ECE-2025 Spring-04 jMc 3 Quiz 3 Histogram 4/14/2004 ECE-2025 Spring-04 jMc 4 PeZ Demo: Pole-Zero Placing Lecture
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4/14/2004 ECE-2025 Spring-04 jMc 5 READING ASSIGNMENTS ± This Lecture: ± Chapter 8, Sects. 8-4 8-5 & 8-6 ± Other Reading: ± Recitation: Chapter 8, all ± POLE-ZERO PLOTS 4/14/2004 ECE-2025 Spring-04 jMc 6 LECTURE OBJECTIVES ± SYSTEM FUNCTION: H(z) ± H(z) has POLES and ZEROS ± FREQUENCY RESPONSE of IIR ± Get H(z) first ± THREE-DOMAIN APPROACH ω ˆ ) ( ) ( ˆ j e z j z H e H = = ) ( ) ( ] [ ˆ j e H z H n h 4/14/2004 ECE-2025 Spring-04 jMc 7 THREE DOMAINS Z-TRANSFORM-DOMAIN POLYNOMIALS: H(z) FREQ-DOMAIN A A A ˆ 1 ˆ 0 ˆ 1 ) ( j N k j M k k j e a e b e H = = = TIME-DOMAIN = = + = M k k N k n x b n y a n y 0 1 ] [ ] [ ] [ A A A } , { k b a A Use H(z) to get Freq. Response z = e j ˆ ω 4/14/2004 ECE-2025 Spring-04 jMc 8 H(z) = z-Transform{ h[n] } ± FIRST-ORDER IIR FILTER: y [ n ] = a 1 y [ n 1] + b 0 x [ n ] H ( z ) = b 0 1 a 1 z 1 ] [ ) ( ] [ 1 0 n u a b n h n =
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4/14/2004 ECE-2025 Spring-04 jMc 9 Typical IMPULSE Response h [ n ] = b 0 ( a 1 ) n u [ n ] = 3(0.8) n u [ n ] 4/14/2004 ECE-2025 Spring-04 jMc 10 First-Order Transform Pair
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2025-L24 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW Quiz...

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