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SPFirst-L14

# SPFirst-L14 - Signal Processing First READING ASSIGNMENTS...

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8/22/2003 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 14 Z Transforms: Introduction 8/22/2003 © 2003, JH McClellan & RW Schafer 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 8/22/2003 © 2003, JH McClellan & RW Schafer 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 8/22/2003 © 2003, JH McClellan & RW Schafer 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

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8/22/2003 © 2003, JH McClellan & RW Schafer 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] (back to the time domain) ) ( ] [ z X n x ] [ ) ( n x z X
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SPFirst-L14 - Signal Processing First READING ASSIGNMENTS...

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