lecture6-f08

Lecture6-f08 - Administrative EE264 Digital Signal Processing Lecture 6 Polyphase Implementations and Quantization in A-to-D October 8 2008 Ronald

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EE264 Digital Signal Processing Lecture 6 Polyphase Implementations and Quantization in A-to-D October 8, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 2 due on Tuesday, Oct. 7 by 5pm in EE264 drawer on 2 nd floor Packard. HW 3 posted by Oct. 7. • READ: Section 4.6 of DTSP and supplemental notes posted on website. • 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: Sections 4.6 and 4.8 of DTSP • Polyphase implementations • A-to-D conversion • Probabilistic analysis of quantization – Model – Signal-to-noise ratio • Oversampling (if time permits) STANFORD UNIVERSITY, EE264 Polyphase Decomposition of h [ n ] ] [ ] [ k nM h n e k + = = = = = 1 0 1 0 ) ( ) ( ) ( M k k M k M k k k z z E z z H z H
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STANFORD UNIVERSITY, EE264 Polyphase Implementation of h[n] ] [ ] [ k nM h n e k + = = = 1 0 ) ( ) ( M k k M k z z E z H ) ( z H Polyphase implementations are useful when combined with sampling rate changes. STANFORD UNIVERSITY, EE264 Polyphase Decimation - I M ] [ ] [ nM y n w = ) ( z H Downsampling commutes with addition. N multiplies and N -1 additions per output sample (FIR filter). STANFORD UNIVERSITY, EE264 Polyphase Decimation - II M(N/M) multiplies and M(N/M-1) +M-1 adds. Polyphase filters clocked at low rate. STANFORD UNIVERSITY, EE264 Non-Integer ( T’ = TM/L ) Rate Change - I Why should the interpolator go first?
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STANFORD UNIVERSITY, EE264 Non-Integer ( T’ = TM/L ) Rate Change - II x e [ n ] = x [ n / L ], n = 0, ± L , 0, otherwise X e ( e j ω ) = X ( e j L ) ˜ x d [ n ] = ˜ x i [ nM ] ˜ X d ( e j ) = 1 M ˜ X i ( e j ( 2 π r )/ M ) r = 0 M 1 ) ( ) ( ) ( ~ ] [ ] [ ] [ ~ j e j j i k d i e X e H e X k n h k x n x = = −∞ = STANFORD UNIVERSITY, EE264 Non-Integer ( T’ = TM/L ) Rate Change - III X ( e j ) = 1 T X c j T 2 k T k =−∞ X e ( e j ) = X ( e j L ) T T L STANFORD UNIVERSITY, EE264 Non-Integer ( T’ = TM/L ) Rate Change - IV ˜ X d ( e j ) = 1 M ˜ X i ( e j ( 2 r M ) r = 0 M 1 T = 3 T / 2 L T T L T L TM L STANFORD UNIVERSITY, EE264 Can the sampling rate be different between sampling and reconstruction? Problem 4.23 1 1 / 1 s f T = 2 2 / 1 s f T = C/D D/C ) ( t x c ] [ n x ) ( t y c M D/C C/D 1 1 / 1 s f T = 2 2 / 1 s f T = ] [ n x ] [ n x d ) ( t x c ) ( t y
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This note was uploaded on 10/29/2011 for the course EE 246 at Stanford.

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Lecture6-f08 - Administrative EE264 Digital Signal Processing Lecture 6 Polyphase Implementations and Quantization in A-to-D October 8 2008 Ronald

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