I need help with fourier transform

I need help, I was wondering if matlab can do Fourier transforms?

I am trying to transform the following functions:

 f(t)=K*t.*(u(t+a/2)-u(t-a/2));

 f(t)=A*cos(pi*t/2).*(u(t+2)-u(t-2));

 f(t)=A*exp(-2*(t-1)).*u(t-1);

Anything would help. Thank you.

[Matt J]

Symbolically or numerically?

Answer 1

[Youssef Khmou]

hi, John,

You can compute theirs spectrums , the only thing you need is the sample rate , here is an example :

1) Functions :

 % Constants 
 K=2.33;
 A=1.45;
 Fs=20;
 t=0:1/Fs:10;
 a=0.45;
 % Anonymous function
 u=@(t) cos(t)
 f1=K*t.*(u(t+a/2)-u(t-a/2));
 f2=A*cos(pi*t/2).*(u(t+2)-u(t-2));
 f3=A*exp(-2*(t-1)).*u(t-1);
 figure, plot(t,f1,t,f2,'r',t,f3,'g'), legend('f1','f2','f3');
 grid on,

2) Spectrums :

 n=length(f1); % they all have the same length  ..
 N=ceil(log2(n));
 F1=fft(f1,2^N);
 F2=fft(f2,2^N);
 F3=fft(f3,2^N);

 Freq=(Fs/2^N)*(0:2^(N-1)-1);
 figure,
 plot(Freq,abs(F1(1:end/2))), xlabel(' Frequ in Hz'), title(' F1');

 figure,
 plot(Freq,abs(F2(1:end/2))), xlabel(' Frequ in Hz'), title(' F2');

 figure,
 plot(Freq,abs(F3(1:end/2))), xlabel(' Frequ in Hz'), title(' F3');