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Automatic Pitch Tracking. September 18, 2014. The Digitization of Pitch. Praat can give us a representation of speech that looks like:. The blue line represents the fundamental frequency (F0) of the speaker’s voice. Also known as a pitch track

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## Automatic Pitch Tracking

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**Automatic Pitch Tracking**September 18, 2014**The Digitization of Pitch**• Praat can give us a representation of speech that looks like: • The blue line represents the fundamental frequency (F0) of the speaker’s voice. • Also known as a pitch track • How can we automatically “track” F0 in a sample of speech?**Pitch Tracking**• Voicing: • Air flow through vocal folds • Rapid opening and closing due to Bernoulli Effect • Each cycle sends an acoustic shockwave through the vocal tract • …which takes the form of a complex wave. • The rate at which the vocal folds open and close becomes the fundamental frequency (F0) of a voiced sound.**Voicing Bars**Individual glottal pulses**Voicing = Complex Wave**• Note: voicing is not perfectly periodic. • …always some random variation from one cycle to the next. • How can we measure the fundamental frequency of a complex wave?**duration = ???**• The basic idea: figure out the period between successive cycles of the complex wave. • Fundamental frequency = 1 / period**Measuring F0**• To figure out where one cycle ends and the next begins… • The basic idea is to find how well successive “chunks” of a waveform match up with each other. • One period = the length of the chunk that matches up best with the next chunk. • Automatic Pitch Tracking parameters to think about: • Window size (i.e., chunk size) • Step size • Frequency range (= period range)**Window (Chunk) Size**Here’s an example of a small window**Window (Chunk) Size**Here’s an example of a large(r) window**Initial window of the waveform is compared to another window**(of the same duration) at a later point in the waveform**Matching**??? The waveforms in the two windows are compared to see how well they match up. Correlation = measure of how well the two windows match**Autocorrelation**• The measure of correlation = • Sum of the point-by-point products of the two chunks. • The technical name for this is autocorrelation… • because two parts of the same wave are being matched up against each other. • (“auto” = self)**Autocorrelation Example**• Ex: consider window x, with n samples… • What’s its correlation with window y? • (Note: window y must also have n samples) • x1 = first sample of window x • x2 = second sample of window x • … • xn = nth (final) sample of window x • y1 = first sample of window y, etc. • Correlation (R) = x1*y1 + x2* y2 + … + xn* yn • The larger R is, the better the correlation.**By the Numbers**• Sample 1 2 3 4 5 6 • x .8 .3 -.2 -.5 .4 .8 • y -.3 -.1 .1 .3 .1 -.1 • product -.24 -.03 -.02 -.15 .04 -.08 • Sum of products = -.48 • These two chunks are poorly correlated with each other.**By the Numbers, part 2**• Sample 1 2 3 4 5 6 • x .8 .3 -.2 -.5 .4 .8 • z .7 .4 -.1 -.4 .1 .4 • product .56 .12 .02 .2 .04 .32 • Sum of products = 1.26 • These two chunks are well correlated with each other. • (or at least better than the previous pair) • Note: matching peaks count for more than matches close to 0.**Back to (Digital) Reality**??? These two windows are poorly correlated The waveforms in the two windows are compared to see how well they match up. Correlation = measure of how well the two windows match**Next: the pitch tracking algorithm moves further down the**waveform and grabs a new window**“step”**The distance the algorithm moves forward in the waveform is called the step size**Matching, again**??? The next window gets compared to the original.**Matching, again**??? These two windows are also poorly correlated The next window gets compared to the original.**another “step”**The algorithm keeps chugging and, eventually…**Matching, again**??? These two windows are highly correlated The best match is found.**period**The fundamental period can be determined by calculating the length of time between the start of window 1 and the start of (well correlated) window 2.**Mopping up**period • Frequency is 1 / period • Q: How many possible periods does the algorithm need to check? • Frequency range (default in Praat: 75 to 600 Hz)**Moving on**• Another comparison window is selected and the whole process starts over again.**The algorithm ultimately spits out a pitch track.**• This one shows you the F0 value at each step. would I like Uhm A flight to Seattle from Albuquerque Thanks to Chilin Shih for making these materials available**Pitch Tracking in Praat**• Play with F0 range. • Create Pitch Object. • Also go To Manipulation…Pitch. • Also check out:**Summing Up**• Pitch tracking uses three parameters • Window size • Ensures reliability • In Praat, the window size is always three times the longest possible period. • E.g.: 3 X 1/75 = .04 sec. • Step size • For temporal precision • Frequency range • Reduces computational load**Deep Thought Questions**• What might happen if: • The shortest period checked is longer than the fundamental period? • AND two fundamental periods fit inside a window? • Potential Problem #1: Pitch Halving • The pitch tracker thinks the fundamental period is twice as long as it is in reality. • It estimates F0 to be half of its actual value**Pitch Halving**pitch is halved Check out normal file in Praat.**More Deep Thoughts**• What might happen if: • The shortest period checked is less than half of the fundamental period? • AND the second half of the fundamental cycle is very similar to the first? • Potential Problem #2: Pitch doubling • The pitch tracker thinks the fundamental period is half as long as it actually is. • It estimates the F0 to be twice as high as it is in reality.**Pitch Doubling**pitch is doubled**Microperturbations**• Another problem: • Speech waveforms are partly shaped by the type of segment being produced. • Pitch tracking can become erratic at the juncture of two segments. • In particular: • voiced to voiceless segments • sonorants to obstruents • These discontinuities in F0 are known as microperturbations. • Also: transitions between modal and creaky voicing tend to be problematic.

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