Joshua Dean
Laboratory 01: Introduction to MATLAB
Lab 02b: Introduction to Complex Exponentials Direction Finding
February 5, 2011
The George Washington University
School of Engineering and Applied Science
ECE 3220
Design of Logic Systems
Lab Section 30
Damon Conover
80/100
Lab 1:
[20/20]
Plot x
1
, x
2
, and x
3
[10/20]
Measure A
1
, tm
1
, A
2
, tm
2
, A
3
, and tm
3
Calculate φ
1
, φ
2
, and φ
3
Use phasor addition to compute A
3
` and φ
3
` (compare with A
3
and φ
3
)
[8/10]
Matlab code for complexamplitude representation of x
1
(t)
Lab 2b:
[2/10]
Plot x(t), measure f, φ, and A
Use phasor addition to compute A` and φ` (compare with A and φ)
[20/20]
Compute t1 (xv) and t2 (xv), plot x1(t) and x2(t) when xv = 100 m
[20/20]
Compute θ and true θ (from DF_GEN), plot both on same graph, and compare
Laboratory 01: Introduction to MATLAB
1.
Introduction
The purpose of this lab was to gain elementary understanding of a few of MATLAB’s
functions, such as arithmetic, complex mathematics, vectors, matrices, and sinusoid
representations of digital signals.
The lab shows how MATLAB works with matrices to
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create a more easily understandable result for the user to analyze. The lab also shows how
MATLAB can be utilized in the representation of digital signals.
The first section of the lab asked to graph two sinusoidal waves, and then graph their
sum.
The lab then asked to graph the maxima of the wave in attempt to calculate the
phase shift.
This was possible because the horizontal component of the peak can show
the time shift of the cosine waveform.
Then the phasors were added together.
The next step was to write a one line code that would generate the same values.
This was
done by using the complex amplitude representation containing the constants of Ω and x.
2.
Matlab Code
Sinusoids
T=0.00025;
%this designates the period of the waveforms
tt= T:T/25:T;
%this gives 25 samples per second
a1=19;
%my age was set as the amplitude for the first wave
a2=a1*1.2;
%my age was multiplied by 1.2 for amplitude of the second wave
x1=a1*cos(2*pi*4000*(tt((37.2/2)*T)));
%sinusoidal waveform x1
subplot(2,2,1), plot(tt,x1, 'b'),
%plotted the waveform with use of the
subplot function to make a 2x2 matrix
title('TEST PLOT for x1'), grid on
%added title and grid to the graph
xlabel('TIME (sec)')
%labeled x axis
legend('x1')
%set legend for x axis
ylabel('AMPLITUDE of x1')
%labeled y axis
x2=a2*cos(2*pi*4000*(tt((41.3/12)*T)));
% set sinusoidal waveform x2
subplot(2,2,2), plot( tt, x2, 'r')
% plotted the waveform with use of the
subplot function to make a 2x2 matrix
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 Fall '11
 Conover
 Digital Signal Processing, Signal Processing, Complex number, Sine wave, Joshua Dean, LAB2b Damon Conover, Joshua Dean ECE

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