# Polyphonic pitch recognition algorithm??

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I've been dying to find an algorithm to convert a PCM input to MIDI. MIDI format isn't as important as simply knowing what notes are played. Can anyone help me?? Google gave me a GNU project ( https://gna.org/projects/fanr ), and I might try extracting the algorithm itself from that. If there's already a mathy approach available, though, I'm all ears. Thanks in advance!

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fourier transform

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Pitch detection algorithm has a decent survey of techniques.

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Wowee! Fourier transforms seem to hit the spot perfectly! Thanks bunches! I'll also look into the PDA. I really appreciate ya'lls' help!

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EDIT - revised the code

Alright, I think I'm getting closer.

I'm pulling heavily from: http://student.kuleuven.be/~m0216922/CG/fourier.html so forgive me if I'm making rookie mistakes here.

data[] is an int array, num is the length of data, hi and lofrequencies[] are double arrays containing acceptable frequency ranges for the 88 keys on a piano. The imaginary part of data[] is 0, so I simplified the code from the site a bit.

I only calculated the FTs for the frequencies I'm looking for (or at least, that's what I hope the code does), so that's what the for(w = ...) is all about.

	public double[] getAmps(int[] data, int num)	{		double[] FRe = new double[num];		double[] FIm = new double[num];		double[] FAmp = new double[num];		double[] ampReal = new double[88];		for(int j = 0; j < 88; j++)		{			ampReal[j] = 0;			for(int w = (int)(sampleRate/hifrequencies[j] - 0.5); w < (int)(sampleRate/lofrequencies[j] + 0.5); w++)			{				FRe[w] = 0;				FIm[w] = 0;				for(int x = 0; x < num; x++)				{					double a = -2 * Math.PI * w * x / (double)(num);					double ca = Math.cos(a);					double sa = Math.sin(a);					FRe[w] += data[x] * ca;					FIm[w] += data[x] * sa;				}				FRe[w] /= num;				FIm[w] /= num;				FAmp[w] = Math.sqrt(FRe[w] * FRe[w] + FIm[w] * FIm[w]);				ampReal[j] += FAmp[w];			}			ampReal[j] /= ((int)(sampleRate/lofrequencies[j] + 0.5) - (int)(sampleRate/hifrequencies[j] - 0.5));		}				return ampReal;	}

[Edited by - SirGorthon on August 15, 2008 3:08:20 PM]

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I'm not sure that the Fourier Transform is the right tool for this job.

I think the Goertzel algorithm is probably the better choice:
http://en.wikipedia.org/wiki/Goertzel_algorithm

The real benefit to using the Fourier transform, when it is appropriate, is that you can do an O(nlogn) FFT instead of the naive O(n^2) algorithm. But if you only need a few frequencies -- say, 'm' of them -- then the naive method can again be faster because it's O(m n). So, clearly, there's a tradeoff. When m is small, the O(m n) algorithm is faster, but when it's large, you might as well increase m to n (i.e., compute all the frequencies), and then use the O(nlogn) algorithm.

The Goertzel algorithm improves slightly on the naive algorithm. It has the same asymptotic complexity, but has better constants.

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