lecture12-f08

# Lecture12-f08 - Administrative EE264 Digital Signal Processing Lecture 12 Digital Filter Design November 3 2008 Ronald W Schafer Department of

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EE264 Digital Signal Processing Lecture 12 Digital Filter Design November 3, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 5 due on Tuesday, Nov. 4 by 5pm in EE264 drawer on 2 nd floor Packard. • Mid-term exam: – I’m rusty! I’ll try to challenge you more on the final. – Average 89, about half above 90 • READ: Chapter 7. • Review Session: Thursdays 4:15 - 5pm Gates B03 (recording 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 • Discrete-time filtering of continuous-time signals • Setting the specifications • IIR design by bilinear transformation – Butterworth, Chebyshev and elliptic approximations • FIR design by windowing – The Kaiser window • FIR design by mini-max approximation – the Parks-McClellan algorithm • Summary comparison STANFORD UNIVERSITY, EE264 Digital Filtering H eff ( j Ω ) = H ( e j Ω T ), | Ω | < π / T 0, | Ω | > / T H ( e j ω ) = H eff j T ,| | < π

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STANFORD UNIVERSITY, EE264 Setting the Specifications H eff ( j Ω ) = H ( e j Ω T ), | Ω | < π / T 0, | Ω | > / T H ( e j ω ) = H eff j T ,| | < Ω T Ω p T STANFORD UNIVERSITY, EE264 A Design Example • The C-T specifications are ( 1/T= 2000 Hz): • The corresponding D-T specifications are: 0.99 | H eff ( j Ω ) | 1.01, | Ω | 2 (400) | H eff ( j Ω )| 0.001, 2 (600) | Ω | 2 (1000) 0.99 | H ( e j 1.01, | | 0.4 | H ( e j 0.001, 0.6 | | i.e., Ω p = 2 (400) and Ω s = 2 (600). i.e., p p T = 0.4 and s s T = 0.6 . STANFORD UNIVERSITY, EE264 IIR Filter Design • Find B(z) and A(z) so that the filter meets the specifications on the frequency response. H ( z ) = b k z k k = 0 M 1 a k z k k = 1 N = B ( z ) A ( z ) Rational function approximation H ( e j ) = H ( z ) z = e j STANFORD UNIVERSITY, EE264 Rader and Gold Paper C. M. Rader and B. Gold, Proceedings of IEEE, Vol. 55, pp. 149-171, February, 1967.
STANFORD UNIVERSITY, EE264 Ben Gold and Charlie Rader First Kilby Medallists 1997 STANFORD UNIVERSITY, EE264 IIR Design Based on Analog Filters 1. From the specifications on the discrete-time filter, determine an analog filter H c ( s ) such that H ( z ) obtained by meets the specifications. 2. The digital filter is then H ( z ). 3. A large body of results on analog filter approximation can be used to determine H c ( s ). Butterworth Chebyshev Elliptic s = 2 T d 1 z 1 1 + z 1 ; i.e., H ( z ) = H c ( s ) s = 2 T d 1 z 1 1 + z 1 . Bilinear Transformation STANFORD UNIVERSITY, EE264 Bilinear Transformation Method • We simply transform an analog filter H c ( s ) into a digital filter H ( z ) with the following complex mapping: Note that H c ( s ) is NOT the same as H eff ( s ), it is just a filter that we have available that works. More later.

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Lecture12-f08 - Administrative EE264 Digital Signal Processing Lecture 12 Digital Filter Design November 3 2008 Ronald W Schafer Department of

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