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I'm looking for help on pointing me to the right literature....

My question is as follows...

Let's assume I have a discrete function (sinusoidal in nature) sampled at N equi-spaced points. However there is a penalty for each sampling point. After taking the FFT of this function, I usually get a "peaky" signal that has some dominating frequencies.
My application usually requires me to find these dominating frequencies with less interest in their amplitude. Is there literature that looks at how different sampling functions (with less than N equi-spaced samples and not equi-spaced) affect my DFT output? That is, if I'm willing to tolerate certain inaccuracies on the output (and not just by less than N equi-spaced samples), can one come up with a different (non-uniform) sampling function?

Note that I have looked some into the "compressive sampling" literature which notes that a random sampling basis and solving this problem as an optimization problem over the L1-norm is ideal when there is no a priori knowledge of the original function. However, I haven't found the right literature that discusses just how different sampling functions affect one's DFT analysis. This assumes, of course, that one has a FFT method that can handle unequally spaced samples such as the non-uniform discrete Fourier transform (NDFT).

Any wisdom welcomed.

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