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What is the proper way to calculate the frequency content or spectrum of a signal with a variable (but measured) sample rate? I.e. get similar results as you would from an FFT, but for data not evenly spaced in time.

I know I can resample the data by interpolating on an evenly-spaced time vector then apply a FFT, but this seems less than ideal.

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Basically what you have is data which isn't evenly spaced in time.
The conventional way to take care of the is using the Non Uniform Discrete Fourier Transform.

Another approach would be looking at the Fourier Transform as a weighted sum of the signal in time.
Since you know the time shift between the samples you can build the right "Weights" for this kind of sampling. Once you have the weights, all you need is to calculate the weighted sum for each frequency you're interested in.

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