fft of a signal

Hello;

I know I have to use fft for getting the fourier transform of a signal, but I am a bit confused here.

I want to have a plot which shows the amplitude of the fourier transform of a signal vs. the frequency. My signal is a 100x1 matrix, and my sampling frequency was 40Hz. What should I do now?

Answer 1

[Wayne King]

You have to create a meaningful frequency vector to go along with your Fourier transform.

The spacing for the DFT (discrete Fourier transform) frequencies is Fs/N where N is the length and Fs is the sampling frequency.

 Fs = 40;
 t = 0:1/Fs:4-1/Fs;
 x = cos(2*pi*10*t)+randn(size(t));
 xdft = fft(x);

Now to create the frequency vector.

 f = 0:Fs/length(x):Fs/2;

You'll see that the length of f is not equal to the length of xdft.

That's because xdft contains both positive and "negative" frequencies.

We only need 1/2 of xdft because the signal is real-valued.

 xdft = xdft(1:length(x)/2+1);
 plot(f,abs(xdft)); xlabel('Hz');

[Tina]

Thanks but my signal is not something like that you put as x above. My signal is a solution to and ODE, so I dont have the formula for my signal, I just have a matrix now.

[Wayne King]

It does not matter, since I don't have your signal, I made an example for you. If you data is sampled at 40 Hz, then you construct the frequency vector the same way.

Answer 2

[Azzi Abdelmalek]

Example

fs=40
t=0:1/fs:99/fs;
y=rand(1,100);
Yk=fft(y);
N=numel(y)
f=fs*(0:(N-1))/N   %  frequencies
stem(f,abs(Yk))