Hidden Markov modeling of speech using Toeplitz covariance matrices

Abstract Hidden Markov modeling of speech waveforms using structured covariance matrices is studied and applied to recognition of clean and noisy speech signals. This technique allows for easier model adaptation in additive noise than does cepstral modeling of speech. Waveform modeling using autoregressive (AR) structured covariances has been extensively studied and applied previously. However, other covariance structures are possible and here we consider waveform modeling using Toeplitz and circulant structured covariances. We detail maximum likelihood (ML) hidden Markov model training and recognition routines using these matrices, and ML speech gain estimation routines. We show equivalence of asymptotic probabilities of recognition error, under certain conditions, using Toeplitz and circulant matrices to using AR matrices. In experimental results on isolated digits in clean conditions, the Toeplitz covariance structure provides higher performance than the AR structure and has performance similar to that reported in the literature of a cepstral system on the same database. In additive Gaussian noise, we demonstrate superior performance to both the cepstral system and the AR system.

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