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Fundamental frequency


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Fundamental frequency is an estimate of the periodicity of the sound. In the power spectrum it is the lowest common denominator of the harmonic peaks. SAP2011 offers two methods for computing it, to select in Explore & Score, use this radio box:
select_pitch
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Pitch: a measure used in previous versions of Sound Analysis, is a combo-measure of harmonic pitch estimate (cepstrum) and mean frequency. The cepstrum peak is usually calculated upon the spectrum of log spectrum, but instead of log spectrum we use the derivative spectrum. At any given time window, pitch might be either harmonic, sinusoidal (whistle) or not well-defined. In the two later cases, mean frequency provides an appropriate pitch estimate.
Hence, at time window t, we calculate pitch according to three threshold parameters T1, T2, T3.
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ff t =period where FFT(spectral_derivatives t) is the highest. (this is our cepstrum pitch estimate), and then:
if { ff t > T1 || (Wiener entropy < T2 & Goodness of pitch <T3) } Pitch t= mean frequency
Otherwise Pitch t = ff t
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SAP2011 distinguishes between the two based on three considerations: first, harmonic pitch is often frequency bounded, e.g. in zebra finches we rarely see harmonic sounds with a fundamental higher than 1800Hz. Therefore, we reject a cepstral estimate higher than this threshold and prefer the mean frequency estimate.  Second, if the goodness of pitch is very low, pitch is unlikely to be harmonic. Third, if both goodness of pitch and Wiener entropy are low, pitch is even less likely to be harmonic. You can manipulate those parameters in the options. Note that  harmonic pitch is typically low, hence we reject harmonic pitch estimates that are higher than the natural range (e.g., in zebra finch harmonic pitch rarely approaches 2kHz).
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Fundamental frequency (YIN algorithm): This measure is often (but not always) more accurate than the pitch, and it is more computationally expensive (about 40% increase in feature computation time of SAP2011). The algorithm is a so called 'time domain approach', which is based on auto-correlation and does not involve explicit spectral analysis (although auto-correlation and power spectrum and linear transformations of each other). It also include a smoothing algorithm that can, in principle, provide accuracy that might be better than the nyquist limitation by means of interpolation. The only YIN algorithm parameter is minimum frequency. By default SAP2011 set it at 300Hz. For more details, see A. de Cheveigné and H. Kawahara. YIN, a fundamental frequency estimator for speech and music. The Journal of the Acoustical Society of America, 111:1917, 2002. doi:10.1121/1.1458024.
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Pitch version Fundamental frequency comparison: The following examples demonstrate the pros and cons of each approach. As shown, the fundamental frequency estimate is somewhat more accurate and less noisy than the pitch (compare values around the arrows)
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ff_pitch