I'm trying to pick a method to increase the bin-width on several discrete Fourier transforms I'm incorporating into some scientific analysis code. I have several questions about how this could work using Welch's method, and in particular how that would affect the values of the spectral densities and correlation functions one could compute from the Fourier transforms.
Because I'm writing this in C++, and because I care about the amplitude of the spectral density detected (not just correctly detecting a particular frequency) I'm thinking it would be better not to use a windowing function with the sub-transforms; in particular, if the amplitude at a bin matters, then I have to figure out how much averaging the different windowed periodograms together changed the frequency in question, which maybe is simple for someone using functions from a DSP library but may not be so simple for me. If this is a bad idea, or in particular if you're really not supposed to use Welch's method without a windowing function, I'd appreciate understanding that better.
Are there any issues with simply solving for Welch subsample length and number, given a fraction of overlap between Welch subsamples and a desired window width? Aside from the computational expense of this process being less and less rewarding as more resamples are added, are there other issues with shortening the transform in this way?