I've tried to switch from FFT+HPS to chirp-Z using an exponential spacing of sample points to increase the low frequency resolution. After testing, it does seem to produce a more detailed spectrum at lower frame length, however it also seems that the Harmonic Product Spectrum no longer works correctly. I assume that this is because the HPS algorithm may require uniform bin spacing to properly detect periodicity. Since the current algorithm works by stepping through bin indices, my guess is that the fix would be to instead iterate based on frequency values which are then are converted to bin indices, but it seems this could potentially be more inaccurate due to frequencies being converted to fractional bin indices which would then have to be rounded.
For the application of pitch detection, what would the best course of action be here? Abandon using HPS and look for something more suited to the exponential sample distribution, or try to get HPS working with it?
