Homework 12 Solution

# Homework 12 Solution - MEEN 260 Introduction to Engineering...

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MEEN 260 Introduction to Engineering Experimentation Homework 12: Digital Filters Solutions Assigned: Thursday, 17 Apr. 2008 Due: Thursday, 24 Apr. 2008, 9:00 am Homework Problems: Problem 1) Digital Filters Design The following analog signal contains four frequencies, 5, 10, 16, and 25 rad/s and the signal for 0 < t < 20 sec is shown below y= sin(5*t)+0.5*sin(10*t-pi/4)+0.6*sin(16*t-pi/3)+0.25*sin(25*t-pi/6); a) Find the maximum sampling period (minimum sampling frequency) that will not result in aliasing of the given signal. b) Calculate the Nyquist frequency, f nyquist for T s = 0.05s and plot the sampled version of the signal of u(t) . c) Design a 3 rd order Butterworth filter for the digitized signal from b), using Matlab command given in the lecture notes with cut off frequency 2 Hz. d) Plot the filtered signal and compare with original signal given in the figure. What conclusion can you make from the comparison?

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Solution: a) The maximum sampling period which will not result in aliasing is twice the maximum frequency of the components of the combined summation of signals.
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Homework 12 Solution - MEEN 260 Introduction to Engineering...

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