sampling rate and fft

Do I need to specify the sampling rate when using FFT? I am wanting to look at frequency response of a signal, and am getting crazy frequency response, way above sampling rate. Sorry for a very basic question, trying to get up to speed.

Answer 1

[Wayne King]

No, you don't need to specify the sampling rate, but if you wish to create a meaning frequency vector, then you need to know the sampling rate.

For example:

    Fs = 1000; % sampling rate of 1000 Hz
    t = 0:1/Fs:1-1/Fs;
    x = cos(2*pi*100*t)+randn(size(t));
    xdft = fft(x);
    xdft = xdft(1:length(x)/2+1);
    DF = Fs/length(x); % frequency increment
    freqvec = 0:DF:Fs/2;
    plot(freqvec,abs(xdft))

so the output of fft() is agnostic about frequency, but if you want to interpret that output in physical frequencies, then you need to know the sampling rate.

[Reed]

Thank you. Could you tell me what you are doing with the command

xdft = xdft(1:length(x)/2+1);

I am getting an error in matlab.

[Wayne King]

I am eliminating 1/2 of the fft() output since it is redundant for a real-valued signal if you are just interested in plotting the magnitude.

The syntax above works for an even length signal without warning is your x, your signal an odd number of samples in length?

If that is the case, do

xdft = xdft(1:floor(length(x)/2)+1);

[Reed]

Thank you very much. makes sense, I'm a little slow with this sometimes :(