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

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"); 

Answer 1

[Prasanna Konyala]

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.