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# HW10_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 10 Prof. Bresler, Prof. Jones Wednesday, October 29, 2008 Problem 1 A speech signal x a ( t ) is assumed to be a bandlimited to 12kHz. It is desired to filter this signal with a bandpass filter that will pass the frequencies between 300 Hz to 6kHz by using a digital filter H d ( ω ) sandwiched between an A/D and an ideal D/A. (a) Determine the Nyquist sampling rate for the input signal. (b) Sketch the frequency response H d, 1 ( ω ) for the necessary discrete-time filter, when sampling at the Nyquist rate. (c) Find the largest sampling period T for which the A/D, digital filter response ( H d, 2 ( ω )), and D/A can perform the desired filtering function. (Hint: Some amount of aliasing may be permissible during A/D conversion for this part.) (d) For the system using T from part (c), sketch the necessary H d ( ω ). Problem 2 The transfer functions of three LSI systems are given below. For each system, determine if it is a FIR or an IIR filter.

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HW10_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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