**2 Weeks**

A non-periodic signal *x*(*t*)
is described by the following expressions:

Plot this signal
for *t* between 0 and 3 seconds, using enough data points to get a smooth
curve.

Determine the
Fourier Transform for this signal. Using the *linspace* command, create a
frequency vector, and plot the double sided magnitude and phase spectra for the
signal. The range of frequencies should be -50 rad/sec to +50 rad/sec.

The following code can be used to create time and signal vectors for this part of the experiment:

t = linspace(0,3,1201);

x = [ones(1,400) exp(-2*(t(401:1201)-1))];

Plot x vs. t using these commands to be sure that they correctly
plot the original *x*(*t*). Using the *lsim* function, compute
the output signals from 3 different systems with *x*(*t*) as the
input. The syntax for this function with the 3 systems is:

System 1: y1 = lsim(0.2, [1 0.2], x, t);

System 2: y2 = lsim(2, [1 2], x, t);

System 3: y3 = lsim(20, [1 20], x, t);

Plot the 3 output
signals on the same graph as the input signal *x*(*t*). Compare how
closely the each of the output signals matches the input signal.

Document your work in a typed report. Discuss the significance of the particular magnitude and phase plots that were obtained. Discuss your results from passing the input signal through the 3 different systems and how those results are related to the magnitude spectrum for the input signal.

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*Latest revision on
Friday, May 19, 2006 10:55 AM
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