I'm doing a Machine Learning project that incorporates many DSP elements in feature extraction. I am looking at the STFT of a piece of audio and trying to search for specific spectral features within it - for example, the exponential decay of the fundamental frequency of a kick drum - to determine what kind of sound the piece of audio is.
One thing I've looked into is finding the frequencies of all the local maxima of a DFT, unquantized. This includes being able to identify when the peak is "between" bins based on contextual information. A possible path to go down is to find all of the changes in direction within the spectrum, and then for N changes fit an $(N+1)$-degree polynomial using a regression, then finding all the zeroes of the derivative of this polynomial.
But does an algorithm for this already exist? It seems like something that might have been done before.