EEET 3028 University of South Australia Introduction to Communication Systems School of Engineering Practical 1: Signals and Spectra with MATLAB MATLAB is a very convenient programming language for signal processing

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EEET 3028 University of South Australia
Introduction to Communication Systems School of Engineering

Practical 1: Signals and Spectra with MATLAB
MATLAB is a very convenient programming language for signal processing. In this prac-
tical you will learn how to use MATLAB to generate and represent signals in time and
frequency domain, and how to plot them. For more information on MATLAB commands
or functions, you may use the MATLAB documentation or the MATLAB commands help
and lookfor - or one of the many MATLAB tutorials on the internet.
Do the following exercises with MATLAB. For every exercise, write the solution in form
of an m-file. Exercises 1-6 are preparing you for Exercises 7 and 8.

1. Complex numbers

(a) For the complex number x = 1+ j, compute the real part, the imaginary part,
the absolute value and the angle.

(b) For the complex numbers {1,7,-—1,—j}, compute the real part, the imaginary
part, the absolute value and the angle, using vector operations.

2. Function plots

(a) Plot the function y = x? for x € (0, +2].

(b) Plot the function y = x? for x € [0,+2] in green in the same figure.

(c) To above plot, add labels for the axes and grid lines. Add further title and a
legend.

3. Complex exponential function

(a) Plot the function y = sin(2zt) for t € (0, 2.5].

(b) Consider the function x = e/?** for t € [0,2.5]. For this function, plot the real
part, the imaginary part, the absolute value and the angle in four different
subplots in the same figure.

(c) Make a 3D plot of the function x = e/?*' for t € (0,2.5]. Add labels for the
three axes. (And rotate the figure with the mouse.)

4, Plots and sampling period
Consider the signal x(t) = sin(27 fot) for t € [0,27], To = 1/fo and fo = 10° Hz.

(a) Use the sampling period of T, = To/10 (ie. 10 sample points per Ty seconds)
and plot the signal.

(b) Use the sampling period T, = T)/20 and plot the signal in the same figure (in
a different colour).

(c) Use the sampling period T, = To/4 and plot the signal in the same figure (in a
different colour).

(d) Interpret the results.

Practical 1: Signals and Spectra with MATLAB Page 1

EEET 3028 University of South Australia
Introduction to Communication Systems School of Engineering
5. The rectangular pulse
Consider the rectangular pulse
1 for |t| < 3,
rect(t) = or ltl S 3
0 otherwise.
(a) Write a MATLAB function for rect(t).
(b) Plot rect(t) for t € [—2, 2].
(c) Define the x-axis to go from —3 to +3, and the y-axis to go from —2 to +2.
Label the axes.
6. The sinc-function
Consider the function .
inc(t) sin 7t
sinc(t) = ——.,
nt
and use the corresponding MATLAB function in the following.
(a) Plot the signal s(t) = sinc(fot) for t € [—10T. 107]. fo = 1/To, To = 2. Use
the sampling period T, = T)/10.
(b) Turn on the grid lines in the figure.
(c) Interpret the zeros of s(t).
7. Manipulations of signals
(a) Plot the signal x(t) = 2-sin(27f,t) with f; = 10 Hz.
(b) Plot the signal r2(t) = 2+ 2x,(t).
(c) Plot the signal x(t) = sin(27 ft) with f; = 10f;.
(d) Plot the signal xr4(t) = x,(t) - r3(t).
8. Spectra of signals
Use the MATLAB function ft.m (provided on the course webpage) to compute the
Fourier transform. (This function is only a user-friendly interface to fft.m.)
Write an m-file to perform steps (a) to (c). This will make it easier for you to do
(e), (f), and (g).
(a) Define a sinusoidal signal :r(t).
(b) Compute the Fourier transform X(f) of this signal.
(c) Use a figure with two subplots, and plot the signal in one subplot and its
magnitude spectrum in the other subplot.
(d) Interpret your results.
(e) Change the length of the signal :r(t) and repeat (b), (c), (d).
(f) Change the sampling period of the signal :r(t) and repeat (b), (c), (d).
(g) Define a rectangular signal y(t) and repeat (b), (c), (d).
Practical 1: Signals and Spectra with MATLAB Page 2
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