Theory

 

 

Speech signal can be classified into voiced, unvoiced and silence regions. The near periodic vibration of vocal folds is excitation for the production of voiced speech. The random ...like excitation is present for unvoiced speech. There is noexcitation during silence region. Majority of speech regions are voiced in nature that includevowels,....., semivowels and other voiced components. The voiced regions looks like a near periodic signal in the time domain representation. In a short term .., we may treat the voiced speech segments to be periodic for all practical analysis and processing. The periodicity associated with such segmentsis defined is 'pitch period T_o' in the time domain and 'Pitch frequency or Fundamental Frequency F_o' in the frequency domain. Unless specified, the term 'pitch' refers to the fundamental frequency ' F_o'. Pitch is an important attribute of voiced speech. It contains speaker-specific information. It is also needed for speech coding task. Thus estimation of pitch is one of the important issue in speech processing.

 

There are a large set of methods that have been developed in the speech processing area for the estimation of pitch. Among them the three mostly used methods include, autocorrelation of speech, cepstrum pitch determination and single inverse .... technique (SIFT) pitch estimation. One success of these methods is due to the involvment of simple steps for theestimation of pitch. Even though autocorrelation method is of theoritical interest, it produce a frame work for SIFT methods.

 

 

Pitch estimation by Autocorrelation method

 

 

Fig.1

 

 

The information about pitch period 'T_o' is more pronounced in the autocorrelation sequence of voiced speech compared to the speech segment itsely. Fig 1 shows a 30 msec segment of voiced speech and its autocorrelation sequence. Since autocorrelation sequence is symmetric with respect to zero lag, only postiove lag values are shown in the figure. The 'T_o' information is more pronounced in the autocorrelation sequence compared to speech. By that we mean, the second largest peak is the autocorrelation sequence, represents T_o and
can be picked up easily by a simple peak picking algorithm compared to finding 'T_o' from the speech segment itself. Hence autocorrelation method is preferred over other direct methods of pitch estimation from speech.

 

Fig.2

 

 

Fig.3

 

 

Fig 2 shows a 30 msec segment of unvoiced speech and its autocorrelation sequence. There is no prominent peak as in the case of voiced speech. This is the fundamental distinction between voiced and unvoiced speech. Further, human speech pitch is typically in the range 100-400 H_z and accordingly the pitch in the range 2.5-10 msec. Therefore for the estimation of pitch the largest peak in the partial autocorrelation sequence starting from 2.5 msec lag is ..... out and its distance with respect to zero lag is measured as pitch peak 'T_o '. This is illustrated in Fig 3. Once we know T_o , then pitch can be computed as ..... , where F_s isthe sampling frequency of the speech signal and 'T_o ' is pitch period in samples.

 

For instance, if T_o = 10 msec, F_s  = 8000 H_z , then T₀ in samples= 10*8=80. F₀ = 8000/80 = 100 H_z 

 

 

Cepstrum Pitch Determination

 

The main limitation of pitch estimation by the auto correlation of speech is that there may be peaks larger than the peak corresponding to the pitch period T₀ due to the .... of the vocal tract, As a result there may be picking of .... peaks and hence wrong estimation of pitch. The approach to minimize such errors is to separate the vocal tract and excitation source related information in the speech signal and there use the source information for pitch estimation. The ceptral analysis of speech provides such an approach.

 

The ceptrum of speech is defined as the inverse Fourier transform of the log magnitude spectrum. The cepstrum projects all the slowly varying components in log magnitude spectrum to the low frequency region and fast varying components to the high frequency regions. In the log magnitude spectrum, the slowly varying components represent the envolope corresponds to the vocal tract and the fast varying components to the excitation source. As a result the vocal tract and excitation source components get represented naturally in the spectrum of speech.

 

 

Fg.4

 

Fig. 4 shows a 30 msec segment of voiced speech, its log magnitude spectrum and ceptrum. The initial few values in the cepstrum typically 13-15 cepstral values represent the vocal tract information. The large peak present after these initial values represent the excitation information. In particular, the pitch period T₀ starting from the zeroth value in number of samples. As a result the peaks that may be occuring in case of autocorrelation analysis get naturally eliminatedin cepstrum pitch determination. Hence the merit of the cepstrum method.

 

 

Fig.5

 

 

Fig. 5 shows a 30 msec segment of unvoiced speech, its log magnitude spectrum and cepstrum. The initial 13-15 values represent the vocal tract information and later ... about the excitation source. By comparing Fig 4 and Fig. 5 it may be observed that there is no prominent peak in case of ceptrum of unvoiced speech after the 13-15 initial cepstral values. This is the main distinction between cepstrum of voiced and unvoiced speech. This observation also ... a method for cepstrum pitch determination. For the estimation of pitch, the target peak in the cepstral sequence after initial 2 msec  .....16 cepstral values, gives the estimation of pitch period in case of voiced speech. This is illustrated in Fig. 6.

 

 

 

 

 

 

The largest peak location in samples gives T₀ and thus pitch is computed as F₀= F_s / T₀. By computing Figs. 6 and Fig. 8, it can be further observe that, the cepstral approach does not have large peaks as in the autocorrelation case that may interfere with the estimation of pitch

 

Pitch estimation by SIFT method:

 

The SIFT method is yet another mostly used pitched estimation method. This is based on the linear prediction (LP) analysis of speech. The SIFT in turn employs the autocorrelation method for the estimation of pitch. However, the main discussion is, it performs autocorrelation of the LP residual than speech directly. For the optimal LP ..., more of the vocal tract information is modeled by the LP coefficients and hence the LP residual mostly contains the excitation source information. The autocorrelation of LP residual will therefore have unambiguous peaks representing the pitch period 'T₀' information.

 

Fig.7

 

 

 

 

Fig.8

 

 

 

 

Figure.9

 

 

 

In case of LP analysis, the vocal tract information is modelled in terms of LP coefficient (LPC) as a process of the prediction of current sample of a combination of ... 'p' samples. The ... LPCs represents the coefficients of the LP filter . The LP filter is the representation of vocal tract. The corresponding inverse filter can be constructed using the inverse property. By passing the speech signal through the inverse filter results in the LP residual as the output. Fig. 7 shows a 30 msec segment of voiced speech, its LP residual and the autocorrelation of the LP residual. As can be observed, there is a prominent peak at the pitch period 'T₀' and there are no other peaks that interfere with its peak. This is the merit of SIFT over autocorrelation of speech.

 Fig. 8 shows 30 msec segment of unvoiced speech, its LP residual and the autocorrelation of the LP residual. There is no prominent peak as in the case of voiced speech shown in Fig. 7 . Thus, a single peak picking can be employed for the estimation of pitch period 'T₀' as illustrated in Fig. 8 . Once 'T₀' is known, then F₀ = F_s/ T₀ , where both F_s and T₀ in samples.

 

Comparision of Pitch estimation methods:

 

 

 

 

 Fig.10

 

 

Fig. 10 shows a 30 msec segment of voiced samples. Its autocorrelation sequence, cepstral sequence and autocorrelation sequence by the SIFT method. All the methods show a peak at the pitch period 'T₀'. Cepstral and the SIFT method sequences have less ambiguity compared to autocorrelation of speech. Hence either cepstrum or SIFT method is equally preferable for the estimation of pitch. In case of speech coding, the mostly used are in LP analysis and hence SIFT method is prefered over Cepstrum pitch estimation. Alternatively, in tasks like speaker recognition, since cepstral analysis is used for the feature extraction tasks, ceptrum pitch estimation may be employed.

 

Fig.11

 

Apart from the avarage pitch value, the other interse is in plotting time varying pitch values resulting in pitch contour information. Fig. 11 shows a speech signal, its pitch contour by autocorrelation of speech, cepstrum and SIFT methods. The random values in the pitch contours compared to the unvoiced and silence regions. The random values in the unvoiced and silence regions. The continuous segments correspond to the voiced regions. Most of the random values can be eliminated by the voiced/ unvoiced classification. In name of the voiced regions, the autocorrelation of speech has same random values due to the sp... peak picking.