Cepstral analysis

The terms cepstrum and cepstral come from inverting the first half of the words spectrum and spectral they were coined because often in cepstral analysis one treats data in the frequency domain as though it were in the time domain, and vice versa. The value of cepstral analysis comes from the observation that the logarithm of the power spectrum of a signal consisting of two echoes has an additive periodic component due to the presence of the two echoes, and therefore the Fourier transform of the logarithm of the power spectrum exhibits a peak at the time interval between them. The... 

An example of the application of the power of cepstral analysis and MEM is illustrated in Fig. 8.11 (b)—(d). The signal in Fig. 8.11(b) was taken from a specimen similar to the one in Fig. 8.10(b), but closer to the edge where the cell was thinner. The overlap of the signals is so great that there is no hope of separating them by eye. The application of cepstral analysis gives the curve shown in... 

A different approach has been applied for the classification of flame images that provides information on the probability of coincidence with each of the combustion states previously known. This procedure is inspired on the cepstral analysis techniques, commonly used for speech recognition [37]. Although sound records are of a type different from image data, both can be equally transformed into covariance matrices, as required in this kind of method. 

Using the cepstrum. As cepstral analysis generates a representation where the pitch information appears as a spike, it is possible to find this spike and determine the pitch from that. 

Imai, S. Cepstral analysis synthesis on the mel frequency scale,. In Proceedings of the International Conference on Acoustics Speech and Signal Processing 1983 (1983), pp. 93-96. 

We will now turn to the important problem of source-filter separation. In general, we wish to do this because the two components of the speech signal have quite different and independent linguistic ftmctions. The source controls the pitch, which is the acoustic correlate of intonation, while the filter controls the spectral envelope and formant positions, which determine which phones are being produced. There are three popular techniques for performing source-filter separation. First we will examine filter-bank analysis in this section, before turning to cepstral analysis and linear prediction in the next sections. 

Separate source and filter tins can be done with cepstral analysis or hnear prediction. 

Figure 14.8 Steps in cepstral analysis, (a) Steps involved in standard cepstral analysis, (b) Steps involved in MFCC-style cepstral analysis.

While cepstral generation via inversion of tiie cepstral analysis technique is possible, it is more common in HMM synthesis to use tiie more direct technique of Mel Logarithmic Spectrum Approximation (MLSA) [229]. This technique is quicker (in that it doesn t require the expensive inverse DFT operations) and can be more accurate at modelling spectral envelopes. MLSA uses more sophisticated signal processing techniques than have so far been introduced and so is beyond our present scope. See however Imai s original paper for details of how this is performed [229]. 

Standard cepstral analysis can be used for a number of purposes, for example FO extraction and spectral envelope determination. One of the main reasons that cepstral coefficients are used for spectral representations is that they are robust and well suited to statistical analysis because the coefficients are to a large extent statistically independent. In synthesis however, measuring the spectral envelope accurately is a critical to good quality and many teclmiques have been proposed for more accurate spectral estimation than classic linear prediction or cepstral analysis. 

One ofthe most widely used techniques is the STRAIGHT set of analysis tools [ ].This system is operates as high quality speech analysis-modification-synthesis method implemented as a channel vocoder and has separate components for instantaneous-ffequency-based FO extraction and pitch-adaptive spectral smoothing. STRAIGHT attempts to obtain a more accurate spectral estimation and a use more sophisticated soiuce model than simple impulses. A comparison of STRAIGHT and standard cepstral analysis is showen in Figure 15.17. 

Koishida, K., Tokuda, K., and Imai, S. CELP coding based on mel cepstral analysis. In Proceeding of the International Conference on Acoustics, Speech, and Signal Processing 1995 (1995). 

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