# hw3 - MEEN 364 Fall 2004 Homework Set 3 Due 5:00 PM Note...

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MEEN 364 Homework Set 3 Fall 2004 September 16, 2004 Homework Set 3– Due September 23, 2004 @ 5:00 PM Note: Clearly label all the plots. Credit will not be given for unlabeled plots. 1. A 10-Hz continuous-time sinusoidal signal corrupted by high-frequency noise, ) 160 cos( ) 140 sin( 3 ) 20 sin( ) ( t t t t x a π π π + + = is sampled at 200 Hz. a) Plot the discrete Fourier transform (DFT)’s magnitude of the sampled discrete- time signal x [n] with respect to frequency (Hint: Use the MATLAB function, ‘fft’) when the continuous-time signal is sampled for (1) 1 s, (2) 10 s, (3) 100 s. Comment on the differences you observe in your plots. (Hint: Visit the website http://www.bores.com/courses/intro/basics/1_resol.htm and read the frequency resolution). b) For three cases of part (a), downsample the signal (Hint: Use the MATLAB function ‘dyaddown’ or ‘downsample’) to a sampling frequency of 100 Hz without passing the signal through a low-pass filter. Plot the magnitude of the resulting DFT with respect to frequency. What do you observe? Is there aliasing? If yes, explain in detail how to obtain the aliased

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