hw4_600(2)

hw4_600(2) - ECE-600 Introduction to Digital Signal...

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Unformatted text preview: ECE-600 Introduction to Digital Signal Processing Autumn 2010 Homework #4 Oct. 15, 2010 HOMEWORK ASSIGNMENT #4 Due Fri. Oct. 22, 2010 (in class) 1. Say that a symmetric real signal x ( t ) = x (- t ) has the CTFT below. For each of the parts below, . f (MHz) X c ( j 2 πf ) 1 1 2- 1- 2 sketch the DTFT X ( e jω ) that results from sampling x ( t ) uniformly at the specified rate. In your sketches, show the range ω ∈ (- 2 π, 2 π ). (a) 1 /T = 12 MHz (b) 1 /T = 6 MHz (c) 1 /T = 3 MHz (d) 1 /T = 2 MHz (e) 1 /T = 1 MHz Hint : Since you know the DTFT phase response for a real-valued symmetric signal, you know how the aliasing copies will add. 2. Say that a signal x ( t ) is sampled at rate 1 /T 1 Hz, producing x [ n ], and then sinc-reconstructed at rate 1 /T 2 Hz, producing y ( t ). Assuming that x ( t ) is bandlimited to 1 2 T 1 , give an expression for Y c ( j Ω) in terms of X c ( j Ω). ( Hint : Relate X c ( j Ω) to X ( e jω ), then relate X ( e jω ) to Y c ( j Ω), and finally relate...
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This note was uploaded on 03/05/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.

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hw4_600(2) - ECE-600 Introduction to Digital Signal...

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