2025-L14

2025-L14 - Info Lab and HW ECE-2025 Spring-2008 Problem...

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ECE-2025 Spring-2008 Lecture 14 Z Transforms: Introduction 10-Oct-08 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 2 Info: Lab and HW Problem Set #8 due NEXT WEEK Sections with recitation on Mo and Tu submit HW at beginning of lab to the grading TAs Quiz #2 on 17-Oct (Friday) – after the break Coverage: HW #5, #6, #7, and #8 One page of Hand-written notes Review Session: Wednesday (15-Oct)? Lab #7 starts Wednesday next week 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 3 READING ASSIGNMENTS This Lecture: Chapter 7, Sects 7-1 through 7-5 Other Reading: Recitation: Ch. 7 CASCADING SYSTEMS Next Lecture: Chapter 7, 7-6 to the end 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 4 LECTURE OBJECTIVES INTRODUCE the Z-TRANSFORM Give Mathematical Definition Show how the H(z) POLYNOMIAL simplifies analysis CONVOLUTION is SIMPLIFIED ! Z-Transform can be applied to FIR Filter: h[n] --> H(z) Signals: x[n] --> X(z) = n n z n h z H ] [ ) ( ) ( ] [ z H n h ) ( ] [ z X n x

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09/30/2008 ECE-2025 Fall-08 jMc-BHJ 5 TWO (no, THREE) DOMAINS Z-TRANSFORM-DOMAIN POLYNOMIALS: H(z) FREQ-DOMAIN k j M k k j e b e H ω ω ˆ 0 ˆ ) ( = = TIME-DOMAIN = = M k k k n x b n y 0 ] [ ] [ } { k b 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 6 TRANSFORM CONCEPT Move to a new domain where OPERATIONS are EASIER & FAMILIAR Use POLYNOMIALS TRANSFORM both ways x[n] ---> X(z) (into the z domain) X(z) ---> x[n]
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