Pitch Period Estimation by Filtering the Fundamental Frequency out of the Speech Waveform

In the past decades a lot of algorithms for estimating the fundamental frequency of speech signals have been proposed. For an overview of the most important ones see Hess (1983). The algorithms either work in the time domain or in the spectral domain. Those working in the spectral domain use a short-term analysis of the speech signal. That is, the average pitch period duration is estimated for (usually overlapping) frames that contain a small number of successive pitch periods. Those working in the time domain estimate a train of laryngeal pulses, which are called pitch markers. Time domain methods have some clear advantages over spectral methods if they work properly. In the first place, they are exact in locating pitch periods, whereas spectral methods can only give estimates of pitch contours and may have difficulty with frames containing both voiced and unvoiced speech. In the second place, a pitch contour derived from a series of pitch markers can be very easily checked by a careful examination of the markers. It can also easily be hand-corrected by removing or adding a number of markers. In the third place, time domain methods can (contrary to spectral methods) be used for pitch synchronous techniques such as pitch synchronous Fourier transformations or the PSOLA-technique with which the prosodic features of speech can be manipulated (Hamon et al., 1989; Charpentier and Moulines, 1989). Recently an interesting time domain pitch extraction method was proposed by Dologlou and Carayannis (1989). They filtered the fundamental frequency out of the (digitized) speech waveform with the iterative use of a lowpass filter (a 3-point Hanning window). Comparing the filtered fundamental frequency with the output signal of a laryngograph, they observed that the points of closure of the vocal chords were very well estimated by the drops in the fundamental frequency signal that were extracted by their method. The crucial part of their algorithm concerns the criterion with which the iterative filtering is terminated. This is done by checking at the end of each iteration whether one or more frequency components are still present in the filtered signal. For this purpose Dologlou and Carayannis use the autocorrelation function and a 2-order LPC analysis which give the same estimate of the frequency of a pure sinusoid; when the difference between these two estimates falls below a predetermined threshold the algorithm stops. However, the assumption that the fundamental frequency is a pure sinusoid is of course not correct, because it is continuously changing. Even within a small stretch of speech (Dologlou and Carayannis used non-overlapping frames of 100 ms) the fundamental frequency varies, so that the threshold they mention should be rather conservative. On the other hand, this might lead to a preliminary ending of the iterations. The problem of choosing a proper threshold is illustrated by the fact that the authors fail to mention which threshold they propose.