HW8 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 310 Digital Signal Processing Problem Set 8 Fall 2003 Due: Wednesday, October 22, 2003 Problem 8.1 A sequence x ( n ) = x a ( nT ), with T = 2 π Ω 0 , is generated from an analog signal x a ( t ) with the following Fourier transform 0 1 X a (Ω) Ω Ω 0 - Ω 0 Ω 0 / 2 - Ω 0 / 2 1. Sketch the DTFT of the sequence x ( n ) = x a ( nT ). 2. In terms of Ω 0 , for what range of values of T can x a ( t ) be reconstructed from the sampled sequence x ( n ) = x a ( nT )? Problem 8.2 An analog LPF H a (Ω) is shown below together with the FT X a (Ω) of an input signal x a ( t ) 0 10kHz 1 -10kHz 1 0 5kHz -5kHz H a (Ω) X a (Ω) Ω 2 π Ω 2 π A digital system is to be designed using uniform sampling and an ideal D/A that will produce the same output as the analog LPF system for the given input x a ( t ). 1
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1. What is the largest sampling period T possible? (note, this system it is possible to
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HW8 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department...

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