3015_Discussion_2_Solutions

3015_Discussion_2_Solutions - University of Minnesota Dept....

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University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #2: Basic signals Complex exponentials (using Matlab) 1. Consider the signal x ( t ) = 2 e j ( t + π /3) a) Find (analytically) its amplitude, phase, real/imaginary part and fundamental period (if periodic). | x ( t )| = 2 arg{ x ( t )} = t + π /3 Re{ x ( t )} = 2cos( t + π /3) Im{ x ( t )} = 2sin( t + π /3) T =2 π b) Using Matlab, plot the amplitude and phase of x ( t ). Show both plots on the same window, one on top of the other, using the command subplot . Label all plots and axes. Scale your time axis so that at least three periods of the signal are plotted. To plot the phase, try two different Matlab commands: phase and angle . What is the difference between these two commands? Is the result consistent with a)? clear all close all t=-3*pi:0.01:3*pi x=2*exp(j*(t+pi/3)); subplot(2,1,1) plot(t,abs(x)) xlabel('Time (s)') ylabel('|x(t)|') title('Amplitude plot') subplot(2,1,2) plot(t,angle(x)) %plot(t,phase(x)) xlabel('Time (s)') ylabel('arg\{x(t)\}') title('Phase plot')
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Command angle plots the signal angle
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3015_Discussion_2_Solutions - University of Minnesota Dept....

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