lecture9-f08

lecture9-f08 - Administrative EE264 Digital Signal...

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EE264 Digital Signal Processing Lecture 9 Linear-Phase Systems and Implementations October 20, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 4 due on Tuesday, Oct. 21 by 5pm in EE264 drawer on 2 nd floor Packard. HW 5 posted by Oct. 21. HW 5 is due on Tues., Nov. 4 . • Mid-term exam: Weds., Oct. 29 in class. – Covers material through Lecture 9 and HW 4. – Open textbook and one 8.5x11 sheet of notes (both sides • READ: Chapter 6 of DTSP . • 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. 9-11am – Rahim: Friday 4-6pm • Grader: Pegah Afshar, Ramin Miri STANFORD UNIVERSITY, EE264 Overview of Lecture • READ: Finish Chapter Chapter 5, read Chapter 6. •R e v i ew : – Minimum-phase systems – Allpass systems • Linear phase systems • Slightly revised course schedule is posted. • Implementation of LTI Systems – IIR structures – FIR structures – Intro to quantization in implementations 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 Allpass Systems • An allpass system has frequency response • The general allpass system has system function • For every pole inside the unit circle there is a zero at the conjugate reciprocal location. H ( e j ω ) = A = constant H ap ( z ) = A z 1 d k 1 d k z 1 k = 1 M r ( z 1 e k )( z 1 e k ) (1 e k z 1 )(1 e k z 1 ) k = 1 M c STANFORD UNIVERSITY, EE264 Example H ap ( z ) = z 1 + 0.75 ( ) z 1 0.5 ( ) z 1 0.8 e j π /4 ( ) z 1 0.8 e j ( ) 1 + 0.75 z 1 () 1 0.5 z 1 1 0.8 e j z 1 1 0.8 e j z 1 ( ) STANFORD UNIVERSITY, EE264 Minimum-Phase Systems • A minimum-phase system is a causal LTI system whose poles and zeros are inside the unit circle.
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lecture9-f08 - Administrative EE264 Digital Signal...

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