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

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