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Homework 14

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Unformatted text preview: EE 4541 Digital Signal Processing Fall 2007 Problem Set 14 Due December 11, 2007 in class Problem 1 Let x[n] be the sequence n , n 0, x[n] = n < 0, 0, where is real, < 1 . We are given another sequence z[n] of length N such that Z [k ] = Y [k ] - e where Y [k ] = X e j -j 2 k N Y [k ], k = 0,1, L, N - 1 ( ) = 2k N , k = 0,1, L , N - 1 obtained through an Npoint IDFT. a) Sketch x[n] and z[n] . Describe the relationship between the two sequences. b) Give an explicit expression for z[n] . c) Suggest an interpretation of the result as filtering operation and identify which samples of z[n] have correct values and which samples (if any) have erroneous values. Problem 2 We are given a lowpass Type I FIR filter, h[n] , with given parameters p , s , p , s . Define g[n] = (- 1) a) b) c) ( M -1) / 2 [n - ( M - 1) / 2] - (- 1)n h[n] What type is the filter g[n] and what is the nature of its frequency response? Express the parameters of the filter g[n] in terms of the parameters of h[n] . Comment on the role of the (- 1) N /2 [n - ( M - 1) / 2] term in this transformation....
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