2025-L13su09

# 2025-L13su09 - ECE2025 Summer 2009 Lecture 13 Z-Transforms...

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1 6/9/2009 1 ECE2025 Summer 2009 Lecture 13 Z-Transforms IIR Filters 22 Jun 09 6/9/2009 3 ANNOUNCEMENTS ± HW #5 due June 22-23 ± June 24-25 ± Turn in Lab #4 ± Do Lab #5 ± Quiz #2 is June 26 (Friday). 6/9/2009 4 SECOND QUIZ ± Quiz #2, in lecture, Friday, June 26 ± 10% of final grade ± You can use the full 1:20-2:30 time ± Review session Thursday June 25, 6pm. ± Emphasis: ± HWs #3 through #5 ± Lectures #5 through #12 ± No Z-transforms, no complete A-D/FIR/D-A cascade ± Closed book, closed notes, except: ± One 8.5”X11” crib sheet allowed, handwritten , OK to write on both sides 6/9/2009 5 READING ASSIGNMENTS ± This Lecture: ± ± Chapter 7

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2 6/9/2009 6 LECTURE OBJECTIVES ± Recap of the Z-TRANSFORM ± Mathematical Definition ± 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 6/9/2009 7 Three Domains: know how to transform among them! 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 6/9/2009 8 TRANSFORM CONCEPT ± Move to a new domain where ± ± 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 6/9/2009 9 “TRANSFORM” EXAMPLE ± Equivalent Representations y [ n ] x [ n ] y [ n ] x [ n ] = n n j j e n h e H ˆ ˆ ] [ ) ( ˆ ˆ 1 ) ( j j e e H = ] 1 [ ] [ ] [ = n n n h δ
3 6/9/2009 10 Z-TRANSFORM IDEA ± POLYNOMIAL REPRESENTATION y [ n ] x [ n ] y [ n ] x [ n ] ) ( z H ] [ n h = n n z n

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## This note was uploaded on 01/24/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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2025-L13su09 - ECE2025 Summer 2009 Lecture 13 Z-Transforms...

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