# Spatial and temporal frequency of a wave

I've sampled a propagating wave so that I know its amplitude at several equidistant points on a line, and at several points in time. That is, I have this discrete function:

f[t,x]


Now, I want to find the frequency of the wave. But there seems to be two frequencies I can calculate: by finding the FFT at different points in time (e.g. FFT{f[1,x]} ) and at different points in space (e.g. FFT{f[t,1]}).

Only the latter ("temporal frequency") gives me a main frequency in Hz. The other one gives one in 1/m, but I suppose that if I knew the wave propagation speed in m/s, I could convert one to the other. Is this true?

All of the above I've just reasoned through myself. Could someone point me to a source where I could read about the two different types of frequency?

Edit: I'll add that the time-space relation is "normal", i.e. the wave propagates like $g(kx-\omega t)$. Hope I'm not being too unclear. I realise that I'm lacking the terminology needed to explain what I mean.

Edit 2: It might be important to know that $f$ is a pulse that is localised in time and space.

Edit 3: I'll put this question here too: Is there a way to take advantage of all the sample points (a 2D matrix) to estimate the central frequency, assuming I know the wave speed?

• I added a quick edit to my answer regarding your 3rd point. – Sam Maloney May 2 '13 at 16:43

Regarding using all the sample points to estimate the wave frequency, I believe you should be able to use the known speed to scale one of your dimensions to match the other, since $distance=velocity*time$. Then a 2D FFT of the matrix should give you information based on all of the available samples in whichever dimension you choose.
• Sam, you imply it but don't come right out and say it: An issue is that the spatial sampling frequency will generally be different from the temporal sampling frequency. So just doing the FFT of F[t,1] and looking for peaks will give a different peak frequency from the FFT of F[1,x]. @Andreas: Do you know what the equidistant distance is? That will help calibrate things. Also, you may need to correct for "approximately equidistant" spatial sampling points. – Peter K. May 2 '13 at 16:52