After we have obtained the pitch from a frame-based approach, it is advisable to perform postprocessing, including
- Smoothing: To smooth the pitch curve such that abrupt-changing pitch are removed.
- Interpolation: To increase the precision of the pitch
One commonly used technique for smoothing the pitch is the median filter, with an order of an odd small intergers, such as 3 or 5. The following example demonstrate the use of a median filter of order 5 to smooth the pitch:
As you can see, the original pitch is full of abrupt-changing noise. After applying a median filter of order 5, some of the noise is correctly replaced with reasonable values. However, for a longer sequence of consecutive error pitch, we still need to rely on other dynamic-programming-based methods to fix them.
To increase the precision of the identified frame-based pitch, we usually apply parabolic interpolation around the maximum of the PDF. In particular, if $n_0$ if the maximizing index of a PDF, then we can fit a pababola that passes three points $(n_0-1, PDF(n_0-1))$, $(n_0, PDF(n_0))$, and $(n_0+1, PDF(n_0+1))$, and then use the maxmizing position of this parabola to compute the pitch. Here is an example:
Audio Signal Processing and Recognition (音訊處理與辨識)