MATLAB: How do i normalise frequency axis after computing fft

Question

i have a 10 hz signal. i want to specify the cutoff for my filter. what is the normalized cut off for 50 hz signal? plz mention the formula used for normalization.

Answer 1

If you have a 50 Hz sampling frequency, the Nyquist frequency — in this instance the normalising frequency if you are designing a digital filter — is 25 Hz. So if you want a 15 Hz cutoff for a lowpass filter for instance, the normalised frequency, ‘Wn’ would be:

Fs = 50;                    % Sampling Frequency (Hz)
Fn = Fs/2;                  % Nyquist Frequency (Hz)
Fc = 15;                    % Cutoff Frequency (Hz)
Wn = Fc/Fn;                 % Normalised Cutoff Frequency (Dimensionless)

So Wn = 15/25 = 0.6

EDIT — For fft scaling, the best documentation is in the R2015a fft version. See specifically the code between the first two plot images.