Hmm. Okay, here's the good news: I've used your code, and it works wonderfully for my purposes. Will be posting a project doc soon on it. This code is probably going to be useful for a number of projects, much praise for doing it, and even more for putting it up here for general use.
The "bad" news is that I'm still a little confused about the function call parameter "m". Note that I am not a mathematics expert- I've simply used your code as a black box audio-range FFT with 64 band resolution, just as you have. I then diddle with outputting the array in various ways. Works great, just working out gain on amplifier for electret mic. It works with a single-stage NPN, but the signals are pretty small.. later today going to add a second NPN (collector direct-coupled, E1-B2 coupled, with and without capacitor, to make a darlington of them) to see if the signal is better.. would be a nice thing if works out to be that easy (doubtful).
I'm trying to understand the underlying math, it's some pretty hardcore stuff.. matrix math and imaginary components.. erm... where's the aspirin? So instead, I'm starting with examining what you have done, to try to get a mental handle on the process from a practical standpoint- as the implementation works, I want to understand WHY it works.
I've got my head around the arrays and why they are needed, but what exactly is "m", in practical terms? It's cryptically referred to as a bit-shift parameter for the data, but that seems wrong too. Is it number of data bits (7 bits, 0-127) in the output array data?
Thanks for any insight, I'm amazed our little arduino can perform a transform reasonably... this code is perfect for my uses, so I want to understand at least the function call parameters, even if the rest remains a Black Box for the time being..
Great work!