PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB
390 Practical MATLAB® Applications for Engineers title (‘Fundamental frequency’); ylabel (‘Amplitude of F1’) subplot (3,2,3); pl ...
Fourier and Laplace 391 − 2 − 1 012 time (in sec) 0.2 −0.2 0 Fifth harmonic Third harmonic 0.5 −0.5− 2 − 1 0 012 − 2 − 1 012 1 − ...
392 Practical MATLAB® Applications for Engineers Harmonic frequencies of f(t) first second third fourth fifth 0.8 0.6 0.2 −0.2 − ...
Fourier and Laplace 393 line spectrum frequency w (in rad/sec) 0.6 0.4 0.2 0.25 0.2 0.15 0.1 0.05 −0.2 Amplitude of Fn^0 − 20 − ...
394 Practical MATLAB® Applications for Engineers syms coesquare expon t ; for k =1:5 expon = exp(-j*k*w0*t); coesquare = .5*int( ...
Fourier and Laplace 395 ANALYTICAL Solution The coeffi cients of the exponential FS for f(t) are given by F T n n n sin( ...
396 Practical MATLAB® Applications for Engineers The script fi le square_time_frq is executed and the spectrums of the pulses fo ...
Fourier and Laplace 397 Create the script fi le Fourier_ approx that returns the following: The plots of the approximation for ...
398 Practical MATLAB® Applications for Engineers xlabel('time (in sec)') title('4 term approximation ') minft26 = min(ft26); max ...
Fourier and Laplace 399 26 term approximation 1 0.5 0.5 − 3 − 3 − 2 − 2 − 1 − 1 0 0 1 1 0 0 Amplitude Amplitude Amplitude 2 2 3 ...
400 Practical MATLAB® Applications for Engineers Example 4.8 Evaluate by hand the FT (non-periodic) of the rectangular pulse f( ...
Fourier and Laplace 401 F10 =10*sin(w*tau10/2)./(w*tau10/2); subplot(3,1,1) plot(w,F1); ylabel(‘Amplitude’); title(‘Spectrum of ...
402 Practical MATLAB® Applications for Engineers % Script file: square _ FT _ sym % This file returns the expressions and plots ...
Fourier and Laplace 403 Example 4.9 Let f(t) = e−^2 tu(t), evaluate by hand The FT of f(t) ↔ F(w), using Table 4.1 The LT of f( ...
404 Practical MATLAB® Applications for Engineers ANALYTICAL Solution Part 1. From Table 4.1, the FT of f(t) = e−^2 tu(t) ↔ 1/(jw ...
Fourier and Laplace 405 axis([-5 5 0 0.6]) subplot(2,2,2);plot(w,phase*180/pi) xlabel(‘frequency w’);ylabel(‘Angle in degrees’) ...
406 Practical MATLAB® Applications for Engineers ***************************************** ************************************* ...
Fourier and Laplace 407 − (^50) 0.1 0.2 0.3 0.4 0.5 0.6 5 − 5 0 0 0.2 0.4 5 − 10 − 100 − 50 50 100 − 5 frequency s Magnitude of ...
408 Practical MATLAB® Applications for Engineers Example 4.10 Analyze by hand and using MATLAB (include pretty) the block box sy ...
Fourier and Laplace 409 xw =2*pi*sin(w*pi)./(w*pi); % FT of x(t) from Table 4.1,transf.#3 % H(w) = 6/(w^2+9); % FT of h(t) from ...
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