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Unformatted text preview: ECE-600 Introduction to Digital Signal Processing Winter 2011 Homework #4 Feb. 5, 2011 HOMEWORK ASSIGNMENT #4 Due Fri. Feb. 11, 2011 (in class) 1. 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 a simplified expression for Y c ( j ) in terms of X c ( j ). ( Hint : Relate X c ( j ) to X ( e j ), then relate X ( e j ) to Y c ( j ), and finally relate X c ( j ) to Y c ( j ). In doing so, focus on the first Nyquist zone: (- , ). The final relationship should not include a summation of spectral copies!) 2. Suppose again 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 ). Unlike the previous problem, we now allow the possibility of aliasing. But, to simplify matters, we consider the case of real-valued sinusoids....
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