1. Three periodic signals, x₁(t), x₂(t), and x₃(t) are shown. The signal x₃(t) is described by the expression .  The fundamental period for each of these signals is 2 seconds, and they have the same type of symmetry.

• Write a MATLAB script to plot each of these three signals (3 periods each), using enough points to get " smooth" curves. This is just reproducing the curves that I have provided.
• Compute the Fourier series coefficients for each of the signals (if you can find them in the text, that is ok). Plot the single-sided and double-sided spectra for each signal. Include enough frequencies in the plots to adequately represent the frequency content of the signals.
• Plot partial sums of the Fourier series for each of the signals (terms 1 through N in the infinite series). For each signal, decide what N should be to get a "reasonable" reproduction of the corresponding x(t).
• Document this work, comparing the frequency contents of the signals and the numbers of frequencies which appear to be significant to the signals. Include plots to illustrate your work and your conclusions. Include your MATLAB code.

2. Three periodic signals, x₄(t), x₅(t), and x₆(t) are shown (only 1 period for each signal is shown). The fundamental period for each of these signals is 8 seconds.

• Write a MATLAB script to plot each of these three signals (1 period each), using the smallest number of points that will reproduce the curves that I have provided.
• Compute the Fourier series coefficients for each of the signals (they are probably in the text). Plot the single-sided or double-sided spectra for each signal. Include enough frequencies in the plots to adequately represent the frequency content of the signals.
• Redefine your time-domain arrays to represent 1 period of each of these three signals with a time resolution of 0.01 seconds. Apply each signal (one at a time) as the input signal to the LTI system represented by the numerator and denominator polynomials shown below. Plot each input and the corresponding output on the same graph.

num = 1296

den = [1    15.679    122.91    564.44    1296]

3. Document this work, comparing the frequency contents of the signals in terms of the widths of the pulses. Compare the output signals from the LTI system in terms of the input signals’ frequency contents. Discuss how the frequency content of the input signal affects a system’s ability to reproduce that signal at the output. Include plots to illustrate your work and your conclusions. Include your MATLAB code.

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Last revised on Friday, May 19, 2006 10:55 AM