7-8 Postprocessing: Smoothing

After we have obtained the pitch from a frame-based approach, it is advisable to perform postprocessing, including

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:

Example 1: ptWithMedianFilter01.mwaveFile='soo.wav'; opt=pitchTrackBasic('defaultOpt'); opt.frame2pitchOpt.method=2; opt.medianFilterOrder=5; showPlot=1; pitch=pitchTrackBasic(waveFile, opt, showPlot);

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:

Example 2: ptWithParabolicFit01.mwaveFile='soo.wav'; opt=pitchTrackBasic('defaultOpt'); pitch1=pitchTrackBasic(waveFile, opt); opt.frame2pitchOpt.useParabolicFit=1; pitch2=pitchTrackBasic(waveFile, opt); subplot(211); plot(1:length(pitch1), pitch1, 1:length(pitch2), pitch2); legend('Original pitch', 'Finetuned pitch with parabolic fit'); subplot(212); plot(1:length(pitch1), pitch1-pitch2); title('Pitch difference');

Audio Signal Processing and Recognition (音訊處理與辨識)