Homework 8

Homework 8

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Unformatted text preview: EE 4541 Digital Signal Processing Fall 2007 Problem Set 8 Due: November 1, 2007 1. In the system shown below, H e j ( ) - j 4e , = 0, | | < 8 8 <| | < a) (10 points) Sketch the spectra of v[n] , w[n] , and y[n] given the spectrum of x[n] shown in the figure. b) Assuming x[n] = xc (nT ) , can you express y[n] in terms of xc (nT ) , where T is appropriately chosen based on the upsampling and downsampling factors? If yes, give this relationship. If not, justify your answer. x[n] 4 v[n] h[n] w[n] 6 y[n] 1 X e j ( ) - - 2 2 EE 4541 Digital Signal Processing Fall 2007 Problem Set 8 Due: November 1, 2007 2. Consider the system shown in the figure below. It represents an oversampling A/D system with noise shaping. The noise source, , is an additive model of the quantization source. Read Section 6.6 in P & M for another example of noiseshaping filter in oversampling A/D. a) Express the output Y(z) in the form: Y ( z ) = H x ( z ) X ( z ) + H v ( z )V ( z ) . Find Hx(z) and Hv(z) in terms of H(z). Here we def...
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