I am trying to analyze the musics as possible as precisely. Of course I tried FFT, but got some problems.
I found low frequencies have very low resolution than human's hearing. I tried very long time FFT to resolve this problem, but even analyzing with 8192 samples/s in 44100Hz sample rate(Means lack of time resolution), I got not enough resolution on low frequencies.
I found there are few solutions.
Firstly, a quadratic interpolation on FFT bins.
But it seems not a perfect way. Problems of this method are:
1. 'If i want to determine freqs between the freq bins, which three bins should I select to do an interpolation?'
2. 'Even I do this, there are no actual additional informations on result. I know interpolations are kind of tricky method.'
Secondly, extracting each freq bins with desired frequency, so I can extract the bins logarithmically.
But have a critical computational cost problem: (maybe over)N^2.
Thirdly, LFT(Logarithmic Fourier Transform).
This requiers logarithmically-spaced samples and gives me result exactly what I looking for with incredibly fast speed; https://stackoverflow.com/questions/1120422/is-there-an-fft-that-uses-a-logarithmic-division-of-frequency
But I have no idea with that algorithm. I tried to understand the paper and implement it, but it was impossible because of lack of my english and mathematical skills.
So, I need a help of implementation of LFT.