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# HW10 - H d ω = R ω e-j ωM β with R ω real are called...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 310 Digital Signal Processing Problem Set 10 Fall 2003 Due: Wednesday, November 5, 2003 Problem 10.1 A CD-player reproduces a signal having a 20 kHz bandwidth from samples originally collected at 44,100 samples per second. If the D/A uses oversampling by L , find the beginning and end of the transition band for the following compensation filter F a (Ω) for: (a) L = 6, (b) L = 10. Problem 10.2 Given x n is the input, let v n be the output of the up-sampler by L , and w n be the output of the down-sampler by D . We know that X d ( ω ) = braceleftBigg 1 - 2 | ω | π if | ω | ≤ π/ 2 0 if π/ 2 < | ω | ≤ π 1. Sketch V d ( ω ) for L = 2 2. Sketch V d ( ω ) for L = 3 3. Sketch W d ( ω ) for D = 2 4. Sketch W d ( ω ) for D = 3 Problem 10.3 Recall that frequency responses of the form

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Unformatted text preview: H d ( ω ) = R ( ω ) e-j ( ωM + β ) with R ( ω ) real are called generalized linear phase . Determine whether each of the following unit-pulse responses corresponds to a generalized linear phase ±lter. If so, then ±nd R ( ω ), M , and β , and indicate whether each unit-pulse response corresponds to a linear phase ±lter. 1. { h ( n ) } 2 n =0 = { 2 , 1 , 2 } 2. { h ( n ) } 2 n =0 = { 1 , 2 , 3 } 1 3. { h ( n ) } 2 n =0 = {-1 , 3 , 1 } 4. { h ( n ) } 4 n =0 = { 1 , 1 , 1 ,-1 ,-1 } 5. { h ( n ) } 3 n =0 = { , 1 , ,-1 } 6. { h ( n ) } 3 n =0 = { 2 , 1 , 1 , 2 } In each case, the remaining terms of the unit-pulse response of the Flter are zero. 2...
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