¿A que se debe que en el comienzo las gráficas no sean iguales?

Question

Pablo Álvarez García 2022-2-12

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回答： Prasanna Konyala 2022-2-18

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Why is it that at the beginning the graphs are not equal? One is Laplace, one is Fourier.

%% 5

%Transformada de Fourier

close all

clear all

syms t s w

Gs=1/(s^2+5*s+6);

Gjw=subs(Gs,s,j*w);

U=cos(pi*t/4).*cos(pi*t/3);

Ujw=fourier(U);

Yjw=Gjw*Ujw;

y=ifourier(Yjw,w,t);

time=0:0.01:50;

yyf=subs(y,t,time);

%Transformada de Laplace

syms t s

Gs=1/(s^2+5*s+6);

U=cos(pi*t/4).*cos(pi*t/3);

Us=laplace(U);

Ys=Gs*Us;

y=ilaplace(Ys,s,t);

time=0:0.01:50;

yyl=subs(y,t,time);

figure(5)

plot(time,yyf,'LineWidth',2); grid on; hold on; plot(time,yyl);

Warning: Imaginary parts of complex X and/or Y arguments ignored.

title("Comparación de las respuestas del sistema");

legend("Fourier","Laplace");

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Answer 1

Prasanna Konyala 2022-2-18

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Hi,

From my understanding, you are trying to plot and check output using Fourier and Laplace. The output produced by Fourier transform may not be obtained from Laplace transform by replacing s with jw (e.g: Step function). In this case, the value Ujw is not same as Us when s is replaced by jw. So, the convoluted results Us and Ujw can differ which leads to different outputs at the beginning and is converging as time increases. This is not a MATLAB issue.