lecture8-f08

lecture8-f08 - Administrative EE264 Digital Signal...

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EE264 Digital Signal Processing Lecture 8 Minimum-Phase, All-Pass, and Linear-Phase Systems October 15, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 3 due on Tuesday, Oct. 14 by 5pm in EE264 drawer on 2 nd floor Packard. HW 4 posted by Oct. 14. • READ: Chapter 5 of DTSP . • I will drop your lowest homework grade in figuring the final homework average. • Review Sessions: Thursdays 4:15 - 5pm Gates B03 (available online) • Office Hours: – RWS: Mon./Weds 10-11, and 12:15-12:45 – Raunaq: Mon. 5-7pm, Tues. 1:30-3:30pm – Rahim: Friday 4-6pm • Grader: Pegah Afshar STANFORD UNIVERSITY, EE264 Overview of Lecture • READ: Chapter 5. • Homework No. 3 due on Tuesday, Oct. 14 • Review: Poles and zeros and frequency response – Geometric interpretation • Minimum-phase systems • Allpass systems • Linear phase systems STANFORD UNIVERSITY, EE264 Rational System Functions • Consider a general difference equation of the form • Rational system function of a causal LTI system H ( z ) = b k z k k = 0 M a k z k k = 0 N = b 0 a 0 (1 c k z 1 ) k = 1 M d k z 1 ) k = 1 N Causal z > max d k a k y [ n k ] k = 0 N = b k x [ n k ] k = 0 M Stable max k d k < 1
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STANFORD UNIVERSITY, EE264 Pole-Zero Plot and Frequency Response H ( z ) = (1 re j θ z 1 ) = z re j z H ( e j ω ) = e j re j e j = v 3 v 1 H ( e j ) = e j re j e j = v 3 v 1 = v 3 v 2 = re j v 1 = e j v 1 = v 2 + v 3 v 3 = v 1 v 2 H ( e j ) = H ( z ) z = e j j e z = STANFORD UNIVERSITY, EE264 Example • System function: • Difference equation: • Impulse response: H ( z ) = 1 1 re j z 1 () 1 re j z 1 = 1 1 2 r cos z 1 + r 2 z 2 y [ n ] = 2 r cos y [ n 1] r 2 y [ n 2] + x [ n ] H ( z ) = 1 1 e j 2 1 re j z 1 + 1 1 e j 2 1 re j z 1 ( ) h [ n ] = r n sin n + 1 [] sin u [ n ] STANFORD UNIVERSITY, EE264 Example H ( e j ) = v 3 2 v 1 v 2 H ( z ) = z 2 z re j z re j ( ) j e z = j j j j j j re e re e e e H = 2 ) ( STANFORD UNIVERSITY, EE264 Magnitude π 2
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STANFORD UNIVERSITY, EE264 Phase and Group Delay STANFORD UNIVERSITY, EE264 All-Pass Systems STANFORD UNIVERSITY, EE264 Allpass Systems • An allpass system has frequency response
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This note was uploaded on 10/29/2011 for the course EE 246 at Stanford.

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lecture8-f08 - Administrative EE264 Digital Signal...

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