Abstract
Cepstral analysis of speech has traditionally provided two pieces of information: (1) the cepstral lag, which is a measure of fundamental frequency, and (2) the cepstral peak, which is a measure of the degree of periodicity. Cepstral analysis conveniently separates the effects of the vocal tract from the acoustic source without explicit vocal tract estimation. The cepstral peak of speech is a popular diagnostic tool for voice disorders and vocal treatment assessment, yet the expected value of the cepstral peak has not received sufficient theoretic treatment. Discrete-time analysis of the cepstrum of a periodic pulse train revealed that the cepstral peak is 1/2 for all pulse trains with integer fundamental period T samples. For the more general case of a non-integer period, a pulse train formed with sinc functions produces a cepstral peak of 1/2+ε where the magnitude of ε scales with 1/T. The cepstral peak of various test signals was compared to cepstral peak prominence [Hillenbrand et al., J. Speech Hear. Res. 37, 769–778 (1994)], and accuracy was improved by (1) zero-padding the log spectrum before inverse Fourier transformation, which provides cepstral interpolation, and (2) limiting spectral nulls, which trades off estimate variance and bias.
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