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Lab_01_2b__Introduction_to_Matlab_joshdean_DSP_lab_1_2 -...

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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 complex-amplitude 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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