5.3 Pitch detection algorithms

Autocorrelation algorithm

Theory

To detect the pitch, we take a window of the signal, with a length at least twice as long as the longest period that we might detect. In our case, this corresponded to a length of 1200 samples, given a sampling rate of 44,100 KHz.

Using this section of signal, we generate the autocorrelation function r(s) defined as the sum of the pointwise absolute difference between the two signals over some interval, perhaps 600 points.

Graphically, this corresponds to the following:

Intuitively, it should make sense that as the shift value s begins to reach the fundamental period of the signal T, the difference between the shifted signal and the original signal will begin to decrease. Indeed, we can see this in the plot below, in which the autocorrelation function rapidly approaches zero at the fundamental period.

We can detect this value by differentiating the autocorrelation function and then looking for a change of sign, which yields critical points. We then look at the direction of the sign change across points (positive difference to negative), to take only the minima. We then search for the first minimum below some threshold, i.e. the minimum corresponding to the smallest s. The location of this minimum gives us the fundamental period of the windowed portion of signal, from which we can easily determine the frequency using

Fast-autocorrelation

In generating the r(s) function, we define a domain for s of 0 to 599. This allows for fundamental frequencies between about 50 and 22000 Hz, which works nicely for human voice. However, this does require calculating r(s) 600 times for each window.