iWillApps

One of the major confusions surrounding digital signal processing is the assumption that the peak frequency in the frequency domain will give you an indication of the fundamental frequency (or pitch) of the signal. This is wrong, and in fact no Fourier Transform should be done at all for the best results (at least in my opinion). Wikipedia gives you some idea of the kinds of pitch detection algorithms that can be used on sound (http://en.wikipedia.org/wiki/Pitch_detection_algorithm), and although many ideas are discussed there we will only focus on one, Autocorrelation.

Autocorrelation can be best explained by the cross correlation of the signal itself, and is used to weed out randomization in seemingly random data sets (such as an audio signal). To put it basically I've made some C code that calculates the fundamental frequency based on a minimum/maximum frequency lookup, a signal array and its length plus the constant sample rate of the signal (44.1kHz):

#define MIN_FREQ (1.0/(65.406/44100.0))
#define MAX_FREQ (1.0/(1046.502/44100.0))
 
double autoCorrelation(SInt16* samples,int length)
{
	if(length >= MIN_FREQ)
	{
		int lookupCount = MIN_FREQ - MAX_FREQ;
		double* results = (double*) malloc(sizeof(double)*lookupCount);
		for(int p=MAX_FREQ;p<MIN_FREQ;p++)
		{
			double psum = 0.0;
			for(int i=0;i<length-p;i++)
			{
				psum += samples[i]*samples[i+p];
			}
			results[p-MAX_FREQ] = psum / ((double)length);
		}
		double maxFreq = -1.79769313486231E+308;
		int maxIdx = -1;
		for(int i=0;i<lookupCount;i++)
		{
			if(results[i] > maxFreq)
			{
				maxFreq = results[i];
				maxIdx = i;
			}
		}
		free(results);
		return 1.0/((double)(maxIdx+MAX_FREQ)/44100.0);
	}
	return 0.0;
}

I do not recommend calling this function inside a RemoteIO callback, as you will encounter extreme lag towards the start of the application. Instead store the samples from that callback somewhere globally accessible, and then poll a process function using an NSTimer to return you your frequency results.