How to use cepstral?

Question

Recently I asked this question: How to get the fundamental frequency from FFT? (you don't actually need to read it)

My doubt right now it: how to use the cepstral algorithm?

I just don't know how to use it because the only language that I know is ActionScript 3, and for this reason I have few references about the native functions found in C, Java and so on, and how I should implement them on AS. Most articles are about these languages =/ (althought, answers in other languages than AS are welcome, just explain how the script works please)

The articles I found about cepstral to find the fundamental frequency of a FFT result told me that I should do this:

signal → FT → abs() → square → log → FT → abs() → square → power cepstrum

mathematically: |F{log(|F{f(t)}|²)}|²

Important info:

• I am developing a GUITAR TUNER in flash
• This is the first time I am dealing with advanced sound
• I am using an FFT to extract frequency bins from the signal that reaches user's microphone, but I got stuck in getting the fundamental frequency from it

I don't know:

• How to apply a square in an ARRAY (I mean, the data that my FFT gives me is an array. Should I multiply it by itself? ActionScript's debug throws errors when I try to fftResults * fftResults)
• How to apply the "log". I would not know how to apply it even if I had a single number.
• What is the difference between complex cepstral and power cepstral. Also, what of them should I use? I am trying to develop a guitar tuner.

Thanks!

Answer 1

Note that the output of an FFT is an array of complex values, i.e. each bin = re + j*im. I think you can just combine the abs and square operations and calculate re*re + im*im for each bin. This gives you a single positive value for each bin, and obviously you can calculate the log value for each bin quite easily. You then need to do a second FFT on this log squared data and again using the output of this second FFT you will calculate re*re + im*im for each bin. You will then have an array of postive values which will have one or more peaks representing the fundamental frequency or frequencies of your input.