For a one-sided fft, the frequency vector will extend from 0 Hz (DC) to 12.5 Hz (Nyquist frequency) for your signal. The length of the fft (that can be varied with zero padding) controls the frequency resolution, and the frequency resolution is approximately equal to the sampling frequency divided by the length of the fft. (This is exact if the length of the fft is even, and approximate if it is odd, since the length of the fft must be an integer.)
So if the sampling frequency is known (and constant), to get a specific frequency resolution, the length of the fft must be at least:
NFFT = Fs/Fr;
where ‘Fs’ is the sampling frequency and ‘Fr’ is the desired frequency resolution. The fft is more computationally efficient if ‘NFFT’ is an integer power of 2 greater than or equal to the length of the signal.
Fs = 100;
t = linspace(0, Fs-1, Fs)/Fs;
s = sin(2*pi*29*t) + sin(2*pi*30*t);
figure
plot(t,s)
grid
xlabel('Time')
ylabel('Amplitude')
format longG
L = numel(t);
Ts = t(2) - t(1);
Fs = 1/Ts;
Fn = Fs/2;
NFFT1 = 2^nextpow2(L)
Fr1 = Fs/(NFFT1) % Frequency Resolution
FT1s = fft(s,NFFT1)/L;
Fv1 = linspace(0, 1, fix(NFFT1/2)+1)*Fn;
Iv1 = 1:numel(Fv1);
figure
plot(Fv1, abs(FT1s(Iv1))*2)
grid
xlabel('Frequency)')
ylabel('Amplitude')
title(sprintf('Frequency Resolution = %.7f Hz',Fv1(2)))
NFFT2 = 2^(nextpow2(L)+4)
Fr2 = Fs/(NFFT2) % Frequency Resolution
FT2s = fft(s,NFFT2)/L;
Fv2 = linspace(0, 1, fix(NFFT2/2)+1)*Fn;
Iv2 = 1:numel(Fv2);
figure
plot(Fv2, abs(FT2s(Iv2))*2)
grid
xlabel('Frequency)')
ylabel('Amplitude')
title(sprintf('Frequency Resolution = %.7f Hz',Fv2(2)))
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