How to Apply Fourier Analysis with Octave for Signal Transfer Functions?

[MisterSpline]

Hey everyone,
So what I'm trying to do is to find the outgoing signal in function of the time, when
the transfer function of the filter is known and the incoming signal is a periodic piecewise function.
The incoming signal I(t)= 0 for -T/2<t<-T/4
$$=\cos(\frac{t\pi}{T})$$ for -T/4<=t<T/4
= 0 fot T/4<=t<T
And the transfer function I'm using is
$$S(\omega)=\sqrt{10}(\frac{i\omega/\omega_2}{1+i\omega/\omega_2})^2,$$
where $$\omega_2=9301.85 rad/s$$.

I have a solution for the outgoing signal U(t) but I'm not sure I'm doing it right.
This is my source code:

T=1*10^(-3);w2=9301.82; t=-0.005:1/100000:0.005;
y=incoming(t,T); %Sampling my incoming signal
Y=fft(y); %taking the fast Fourier transform
N=length(Y);
freq=[0:N-1];
U=Y.*filter(freq,w2) %where filter is the transfer function
u=ifft(U);
plot(t,ifftshift(u));

 

[Valkarie]

%plotting my outgoing signalCan someone help me out and tell me if this is the right way to do it?Thanks in advance!