# 2025-L15 - ECE-2025 Spring-2009 Info: Quiz, Lab, HW Lab...

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ECE-2025 Spring-2009 Lecture 15 Zeros of H(z) and the Frequency Domain 2-March-09 fo: uiz Lab HW Info: Quiz, Lab, HW uiz #2 on 9 arch (Monday) ± Quiz #2 on 9-March (Monday) ± Coverage: HW #5, #6, #7, and #8 ± One page of Hand-written notes ± Review Session: Sunday (8-March) ± ECE Auditorium, 6pm ± Sampling, FIR filters, Frequency Response 2/28/2009 ECE-2025 Spring-09 jMc 2 Lecture EADING ASSIGNMENTS READING ASSIGNMENTS ± This Lecture: ± Chapter 7, Section 7-6 to end ± ther Reading: Other Reading: ± Recitation & Lab: Chapter 7 ± EROS (and POLES) ZEROS (and POLES) ± Next Lecture:Chapter 8 2/28/2009 ECE-2025 Fall-04 jMc 3 ECTURE OBJECTIVES LECTURE OBJECTIVES ± ZEROS and POLES ± Relate H(z) to FREQUENCY RESPONSE ω ˆ ) ( ) ( ˆ j j z H e H = = ± THREE DOMAINS: how Relationship for FIR: e z ± Show Relationship for FIR: ) ( ) ( ] [ ˆ j e H z H n h 2/28/2009 ECE-2025 Fall-04 jMc 4

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ESIGN PROBLEM DESIGN PROBLEM ± Example: ± Design a Lowpass FIR filter (Find b k ) ± Reject completely 0.7 π , 0.8 π , and 0.9 π ± This is NULLING ± Estimate the filter length needed to accomplish this task. How many b k ? ± Z POLYNOMIALS provide the TOOLS 2/28/2009 ECE-2025 Fall-04 jMc 5 ransform DEFINITION Z-Transform DEFINITION OLYNOMIAL Representation of LTI ± POLYNOMIAL Representation of LTI SYSTEM: = n z n h z H ] [ ) ( ± EXAMPLE: n APPLIES to ny SIGNAL Any SIGNAL 4 3 2 1 0 = } 2 , 0 , 3 , 0 , 2 { ]} [ { = n h POLYNOMIAL in z -1 2 0 3 0 2 ) ( + + + z z z z z z H 4 2 2 3 2 + = z z 2/28/2009 ECE-2025 Fall-04 jMc 6 4 1 2 1 ) ( 2 ) ( 3 2 + = z z
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## This note was uploaded on 01/27/2011 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Institute of Technology.

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2025-L15 - ECE-2025 Spring-2009 Info: Quiz, Lab, HW Lab...

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