Signals and System: MATLAB code provided?
Begin with the MATLAB script named lab4.m as follows. You will modify this example code to cover each of the parts of this lab. You must always carefully document and include appropriate comments in any MATLAB code. & starting point for Lab#4 % LAPLACE TRANSFORM %———- clear all; close all; ——————– s = tf(‘s’); sys = 1/(5+1); & define H(s) for a dynamic system named sys —————- figure(1); bode (sys); % plot magnitude and phase grid on; saveas (gcf, ‘lab7a.png’); figure(2); impulse (sys); plot impulse response grid on; axis ([-3 6 -1 2]); saveas (gcf, ‘lab7b.png’); figure(3); pzmap (sys); & plot pole zero diagram axis ([-2 2 -2 2]); saveas (gcf, ‘lab7c.png’); figure (4); t = 0:0.001:10; s = cos(2*pi*t); lsim(sys,s,t); $ plot response for arbitrary input grid on; axis ( [0 5 -2 2]); saveas (gcf, ‘lab7d.png’); ——– % END 1. Beginning with the starting code above, confirm the form of the impulse response h(t) for the first order system H(S) as given. From the pole zero diagram, confirm that the single pole lies on the left hand plane at (0,jo)=(-1,0) Plot the exponential curve corresponding to this h(t) directly from the pole position as: sigma = -1; t = 0:0.01:6; h = exp (sigma*t); figure(5); plot(t,h); grid on; Confirm that this plot matches the h(t) found using impulse(sys). Choose two time points on the curve and verify that the same amplitude is found in both graphs. 2. Consider two poles located on the vertical axis at (,jo)=(0,+1) and (0,jo)=(0,-1) as defined by: H(s)= 1 Use MATLAB to define the system H(s) given these poles as: omega = 1; sys = zpk((,[j*omega,-j*omega], omega) From the above command, confirm the form of H(s). Plot the impulse response h(t). What is the amplitude and period of this h(t)? Is this a stable system? Plot the sinusoid corresponding to this h(t) directly from the pole positions as: omega = 1; t = 0:0.01:25; h = sin(omega*t); figure(5); plot(t,h); grid on; Confirm that this plot matches the h(t) found using impulse (sys). It may be useful to rescale this final plot to match the limits on the other.
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