Cepstral distance and the frequency domain
John D. Markel, A. H. Gray · The Journal of the Acoustical Society of America · 1975
Atal [J Acoust. Soc. Am. 55, 1304 (1974)] recently investigated weighted Euclidean distance measures for speaker identification and verification tasks. The cepstral coefficients of the filter A(z) determined through linear prediction analysis resulted in higher scores than other parameters such as predictor coefficients or area functions. The purpose of this paper is to discuss several properties of the cepstral coefficients obtained from A(z) and to suggest that the results illustrate the importance of the smoothed log spectrum as a basis for distance measurements in speech processing. From statistical experiments on speech, it is shown that for very small cepstral lengths (on the order of M, where M is the number of filter coefficients), there exists a very high correlation between the ceptral measure and the root-mean-square (rms) Euclidean distance measure between two log spectral models obtained using linear prediction analysis. Theoretically, an infinite number of cepstral coefficients are necessary for an equality. Since the cepstrum can be recursively evaluated from the filter coefficients [if 1/A(z) is stable], the cepstral distance measure can be viewed as an efficient and accurate replacement for the direct root-mean-square (rms) measure between two log spectra but without FFT or logarithm operations.