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20112ee113_1_Hw7

# 20112ee113_1_Hw7 - X e jω of x n(b Determine the discrete...

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EE113: Digital Signal Processing Spring 2011 Prof. Mihaela van der Schaar (Instructor) Homework #7 Solve the following problems from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing by Prof. A. H. Sayed: Problem 15.1. (You do NOT need to plot the DFT.) Problem 15.6. Problem 17.1. Problem 17.3. In addition, solve the following two problems. Problem A Consider the sequence x [ n ] given by x [ n ] = α n u [ n ], where | α | < 1. A periodic sequence ˜ x [ n ] is constructed from x [ n ] in the following way: ˜ x ( n ) = X r = -∞ x [ n + rN ] . (a) Determine the Fourier transform
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Unformatted text preview: X ( e jω ) of x [ n ]. (b) Determine the discrete Fourier series ˜ X [ k ] of ˜ x [ n ]. (c) How is ˜ X [ k ] related to X ( e jω )? Problem B A real continuous-time signal x c ( t ) is bandlimited to 3kHz, i.e., X c (Ω) = 0 for | Ω | > 2 π (3000). (a) What is the Nyquist sampling frequency of this signal? (b) If the resolution of the DFT is less than or equal to 50 Hz, what should the minimum number of required samples be? What does that number correspond to in msec? 1...
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