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I am trying to post-process pulse train data. It is a 0 to 5V square wave, where the frequency of pulses corresponds to a physical measurement. During measuring, I may see anywhere from 100 pulses/second to 10,000 pulses per second. The duty cycle changes.

I wrote a pulse counter function to analyze the pulse data in the time domain, but the result was very noisy. I suspect that an FFT may be appropriate, though I have never really done anything like this before.

Has anybody done anything similar? What would be the broad methodology behind analyzing the pulse train in the frequency domain? Would it be best to take an FFT at specific time intervals (for instance every seconds worth of data)?

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One idea is to 1) Locate samples that greatly differ from the following sample. That will tell you where the flanks are. 2) Compute time difference between consecutive flanks. 3) Average all those time differences to remove estimation noise (assuming your pulse period is constant throughout the measurement) - Luis Mendo
More information is needed on why you think your pulse counter result is "noisy" and what kind of result you want. For instance, maybe the actual data really is noisy? - hotpaw2

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An FFT might be useful if your pulse train were stationary over some interval (the length of an FFT) and embedded in noise. Otherwise, why not just use at the reciprocal of the time between rising edges?