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- TL;DR Summary
- What are the subtleties when using Fourier analysis?

It has been 35 years since I did the math for Fourier analysis, and I have forgotten what the subtleties are. Please be kind.

So this is not a how do I calculate a DFT (though that may be my next question) but rather how do I use it, and interpret the results.

All the online and software I find seems to use the FFT algorithm.

If I remember properly the FFT requires 2^n samples. I recall you can zero pad to get the samples, but doesn't this change the fundamental frequency/period. eg if I have data for 'm' complete periods I would expect a prominent peak on the m'th harmonic, but if I have zero padded that peak with be scattered across several harmonics, none of which are related to the period in the data ?

What is the FFT calculating anyway? I want the spectrum of a continuous signal. When I multiply this with a comb function (sample) is the FFT calculating the spectrum of the product or the original continuous signal?

Thats all I can put words to at the moment. I have vague recollections that how you choose the data is important but I can't remember how or why.

I look forward to your comments.

So this is not a how do I calculate a DFT (though that may be my next question) but rather how do I use it, and interpret the results.

All the online and software I find seems to use the FFT algorithm.

If I remember properly the FFT requires 2^n samples. I recall you can zero pad to get the samples, but doesn't this change the fundamental frequency/period. eg if I have data for 'm' complete periods I would expect a prominent peak on the m'th harmonic, but if I have zero padded that peak with be scattered across several harmonics, none of which are related to the period in the data ?

What is the FFT calculating anyway? I want the spectrum of a continuous signal. When I multiply this with a comb function (sample) is the FFT calculating the spectrum of the product or the original continuous signal?

Thats all I can put words to at the moment. I have vague recollections that how you choose the data is important but I can't remember how or why.

I look forward to your comments.