# FFT of signals with different sampling frequency

I am trying to combine two sets of data together, each of them having different sampling rates. For example if I sampled a 100 Hz sin wave at 1KSPS, and another 150Hz sin wave at 1.5KSPS, would it be possible to combine them for FFT without using non-uniform FFT techniques? Or would my best case be interpolating the slower one so that they match in sampling rate? Or would it be valid to superposition the result of FFT of the 2 signals for magnitude and phase plots?

(for combining, I mean that I want to do FFT on both signals together such that I see both signals in terms of magnitude and phase plots)

Thank you

• Either zero-pad accordingly signal with lower sampling rate, or use the resampling on one of them. – jojek Aug 18 '14 at 20:56
• @jojek Thank you for your response, can you elaborate on the zero padding? (would that mean to zero pad in the frequency domain? If so, then after zero padding the fft of the slower sampling rate signal, would summing the points yield correct result for magnitude and phase response?) – user8481 Aug 18 '14 at 21:47
• Depending on what you are trying to achieve. If two signals must be fit for comparison in frequency domain, then padding in time domain is a solution. Otherwise, resampling is a way to go. – jojek Aug 18 '14 at 22:21
• @jojek Do you mean that if the signal, say $x(k)$, which is e.g. of 80 samples zero-pad to match the size of 128 and do FFT, result will be the same, as if we resample it with interpolator to the size of 128 and then do FFT? Sorry about so long question =) – Serj Aug 19 '14 at 7:15
• @Serj: No. If you zero pad, take the FT and return back to a time domain, then you will end up with the same signal and lot's of zeros in the end. Reason for zero-padding is one - you have same amount of frequency bins - very easy to compare signals. Another solution is to resample one of the signals and this will give same sampling frequency, thus same number of frequency bins. – jojek Aug 19 '14 at 9:23