PP-delta ("psync")

Voice-related fluctuations are likely to be most harmful in the estimation of the slope of features, as in the $\triangle$- and $\triangle^{2}_{}$-cepstrum. Delta-features are usually calculated by differentiation between primary feature vectors separated by a time shift equal to the analysis step (typically 10ms). Unless the voice period happens to equal to the analysis step (or a fraction of it), the slope estimate will be affected by any residual fluctuation due to insufficient temporal smoothing. The problem will most severe for low F₀s.

Suppose instead that the slopes are calculated by differentiation between feature vectors separated by a period (or a period multiple). Whatever the voice-related fluctuation, it is sampled at a fixed phase with respect to the fundamental period, and the effects on the slope estimate are null. PP-delta features should be less noisy. Not only that, but since one term of the time-resolution compromise is relaxed (see above), there is more freedom to optimize the other. Smoothing of primary features may be less severe, differentiation may be less "smoothing", etc..

F₀can be estimated by any technique, although a lag-domain technique such as AMDF or autocorrelation is advisable (because it is based precisely on a search for a minimum difference between windows spaced a period apart). Integration windows for period estimation and feature extraction should have similar size and shape.

Reliability of period estimation is not an issue. Estimation errors come in two sorts: subharmonic errors (choosing a period multiple instead of the period) and other errors (the estimate is wrong in some other way). The latter type of error occurs when the signal is not very periodic, in which case the PP-delta scheme is of little benefit: one value of the time shift is good as another. To avoid random shifts, the algorithm could decide to use a default shift (for example 10 ms) when periodicity is poor. The former type of error is of no consequence: the scheme works as well if the slope is calculated over a period multiple.

One might object that the PP-delta scheme is most reliable when there is no spectral change! This is true, but it should not prevent it from being useful: the PPD-delta scheme "lowers the noise floor" of the delta features.