Generate frequency-domain abscissa for FFT data.

xf = fdaxis(dT,N)
xf = fdaxis(xt)

This function returns a vector xf of the frequencies of the FFT of a N-point time-domain signal with time step dT. dT can have any unit, the unit of xf is simply its inverse. So for dT in ms, xf is in plain MHz (or Mc in old notation), not in angular frequency units.

In its second call form, the function takes the full time-domain abscissa as input parameter. E.g., xt = (0:10)*0.1 corresponds to dT = 0.1 and N = 11.

The DC component of the FFT abscissa xf is always in the centre. The output of MATLAB's fft returns the DC component as the first element. So be sure that you either apply fftshift to your data after fft or to xf in order to get correct results.

For a 512-point signal tdata sampled with time increments of 8 ns, the frequency domain abscissa in MHz is

N = 512; dT = 0.008; % dT is in microseconds
xf = fdaxis(dT,N); % xf is in MHz

The correct plot of the magnitude FFT of tdata is

tdata = rand(1,N); % a signal with very low SNR ...
fdata = abs(fft(tdata));
plot(xf,fftshift(fdata)); % use of fftshift
xlabel('frequency [MHz]');

The discrete frequencies in the frequency-domain abscissa are apart. The vector always contains the frequency zero, but the start and end frequencies depend on whether N is odd or even.

If N is odd, there is the same number of negative and positive discrete frequencies, and the Nyquist frequency itself is not contained. If N is even, the negative Nyquist frequency is the first element of the vector, and it contains one more negative frequency than positive ones (always excluding zero).

ctafft, evolve