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A simple FFT library for the iPhone, based on Ooura's FFT code. You should now use Apple's built-in Accelerate library. This was made before Accelerate was released, so it's now irrelevant.

branch: master
README
__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
 
 Permission is hereby granted, free of charge, to any person
 obtaining a copy of this software and associated documentation
 files (the "Software"), to deal in the Software without
 restriction, including without limitation the rights to use,
 copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the
 Software is furnished to do so, subject to the following
 conditions:
 
 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 OTHER DEALINGS IN THE SOFTWARE.
 
 
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