__NOTE__
With the release of iOS 4, Apple provides its own built-in FFT functionality in the Accelerate.h framework. USE THAT. ITS SO MUCH FASTER.

* Please read the dope MIT license at the bottom of the page.
 
* The FFT algorithm included was written by Ooura ( http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html ),
so all thanks and questions for the core of this project go in that direction.
 
* This code is in a state of flux. I'm not quite satisfied with its calling conventions,
so function names and data structures will likely be overhauled in the coming months.
But, it does work.
 
* If you use this code in a paid app, please consider donating a little for my time. 
In any case, enjoy!

HOW TO USE:
 
// 1. First initialize the class
OouraFFT *myFFT = [[OouraFFT alloc] initForSignalsOfLength:numFrequencies*2 andNumWindows:kNumFFTWindows];
 
// 2. Then fill up an array with data with your own function
fillUpInputSignalWithMyData(myFFT.inputData);
 
// 3. And then compute the FFT
[myFFT calculateWelchPeriodogramWithNewSignalSegment];
 
// 4. ... then finally, plot the signal with your own function
doSomethingWithTheFrequencyData(myFFT.spectrumData)
 
// Repeat steps 2-4 for any new data you acquire
 
 
WHAT THE HECK KIND OF DATA IS IN "spectrumData"?:
 
OouraFFT.spectrumData contains the frequencies in the signal you plopped into OouraFFT.inputData, then computed by calling calculateWelchPeriodogramWithNewSignalSegment.
Now, which frequencies correspond to which entries in the array?
Say your signal has a sampling rate of 48,000 Hz, and you are computing the FFT on chunks of your signal 1024 samples long. Then, OouraFFT.spectrumData has 1024/2 = 512 frequencies in it, evenly spaced between 0 and 48,000/2 = 24,000. 
 
So, for 0 < i < OouraFFT.numFrequencies, 
spectrumData[i] holds data for (i*samplingRate)/(2*numFrequencies)
 
Why is the highest frequency computed equal to half the sampling rate? This frequency is called the "Nyquist Rate", and frankly, I don't think I can explain it very well. Check out the Wikipedia article for some more info.
 
Hope that helps! 

 Copyright (c) 2009 Alex Wiltschko
 
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