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# hw6_09 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering The Johns Hopkins University 520.137 Introduction to Electrical and Computer Engineering – Fall 2009 Homework Assignment VI Reading Assignment: Kuc Chapter 4 1. Suppose that we would like to sample the following function x ( t ) = 520 cos[5200 π ( t + 1)] + 137 cos(1370 πt + π 8 ) + 2009 sin[20090 π ( t 1)] . (a) Find the sampling rates such that aliasing is guaranteed to be avoided. (b) What is the corresponding sampling period? 2. Consider the following sampling scheme of the pure sinusoid x ( t ) = sin(6 πft ): sampling points are placed at all positive peaks, negative peaks, and all zero-crossings. (a) What is the sampling rate in this case (as a function of f )? (b) How far apart in time are the samples in this case? 3. The audio signal in a telephone line has been band-limited to a maximum frequency of 3 kHz. (a) Determine the sampling rate at which the A/D converter must sample the signal in order to capture an accurate record of it.

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