https://stackoverflow.com/questions/22305359
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RussianI'm not entirely sure why you'd auto correlate the cepstrum. Auto correlation, though, gives you a representation that is related to the cepstrum so I assume you want to just auto correlate your signal.
In its simplest form it is performed as follows:
int sample = 0;
int sampleMax = inSize;
while( sample < sampleMax )
{
vDSP_vsmul( pInput, 1, pInputSample, tempBuffer, 1, sampleMax );
const size_t kAutoCorrWritePos = outSize - sampleMax - sample;
vDSP_vsadd( &pOutput[kAutoCorrWritePos], 1, tempBuffer, 1, &pOutput[kAutoCorrWritePos], 1, sampleMax )
sample++;
}
This is, however, a very slow operation. Thankfully correlation can be performed in several different ways. The fastest method is to perform an FFT, the multiply the complex values by the conjugate of themselves and then inverse fft.
Or in iOS you have the nicely optimised vDSP_conv function:
std::vector< float > paddedBuffer( (inSize + inSize) - 1 );
memcpy( &paddedBuffer.front(), pInput, sizeof( float ) * inSize );
vDSP_conv( &paddedBuffer.front(), 1, (float*)pInput, 1, (float*)pOutput + (inSize - 1), 1, inSize, inSize );
// Reflect the auto correlation for the true output.
int posWrite = (inSize - 1);
int posRead = (inSize - 1);
while( posWrite > 0 )
{
posWrite--;
posRead++;
pOutput[posWrite] = pOutput[posRead];
}
So now you have your auto correlation, what d o you do with it?
Well firstly right in the middle you will have the highest peak. This is the zero lag point. What you then want to do is scan to the right of this central peak to identify the secondary peaks. If yo are looking for a specific peak at a specific offset you can, simply, check the number of samples on from the central peak and check if there is a peak there. If there isn't then the signal you are looking for is not there. If it is there, the signal is there.
Edit: Its worth noting that with a 512 sample wide window if the lag you are looking at is beyond about 128 it may not get enough of a correlation signal to be spottable. The correlation works by providing peaks at points of repetitive signals in the sample data. At a lag of 128 you have enough data for that point to repeat 4 times. At 256 you can only see the point repeat twice. This will affect the height of the correlation peak. After 256 you may not spot the peak at all against just random repeatability factors. That said, though, experiment with different window sizes to see what provides you with the most reliable results.
