lecture5-f08

lecture5-f08 - Administrative EE264 Digital Signal...

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EE264 Digital Signal Processing Lecture 5 Changing the Sampling Rate Using Digital Filtering October 6, 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. • 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 (this week 9- 11am, Packard 109) – Rahim: Friday 4-6pm • Grader: Pegah Afshar STANFORD UNIVERSITY, EE264 Overview of Lecture • Review of DT filtering of CT signals • Anti-aliasing pre-filtering • The need to change sampling rates • Decimation • Interpolation • Changing sampling rate by non-integer factors • Multi-stage decimation and interpolation • Polyphase decomposition of h[n] – Polyphase decimation STANFORD UNIVERSITY, EE264 Sampling Theorem C-to-D Converter x c ( t ) x [ n ] = x c ( nT ) X c ( j Ω ) X ( e j ω ), X ( e j Ω T ) X ( e j Ω T ) = x [ n ] n =−∞ e j Ω Tn = 1 T X c ( j ( Ω− k 2 π T )) k D-to-C Converter x [ n ] = x c ( nT ) x r ( t ) x r ( t ) = x [ n ] sin T t nT () T t nT n ) ( ) ( ) ( T j r r e X j H j X Ω Ω = Ω ) ( ), ( T j j e X e X Ω ) ( Ω j X r
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STANFORD UNIVERSITY, EE264 DT Filtering of CT Signals • If the input is bandlimited such that and then the overall input and output are related by 2 π / T 2 Ω , Y r ( j Ω ) = H ( e j Ω T ) X c ( j Ω ) Ideal D-to-C LTI System Ideal C-to-D x c ( t ) x [ n ] y [ n ] y r ( t ) Y ( e j Ω T ) X ( e j Ω T ) X c ( j Ω ) Y ( j Ω ) Y r ( j Ω ) = H r ( j Ω ) H ( e j Ω T ) 1 T X c ( j ( Ω− k Ω s )) k =−∞
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lecture5-f08 - Administrative EE264 Digital Signal...

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