Probabilistic model of speech with high spectral resolution using maximum-likelihood estimation

Abstract

A probabilistic model for the distribution of narrowband short-time Fourier transform (STFT) coefficients, having frequency resolution of 5 Hz and below, is proposed for speech signals. An important application is to model speech to depict the perceptual stability of human listening capability which allows humans to perceive speech reliably under a wide range of acoustic conditions. Representation of speech with high spectral resolution finds applications in the design of digital hearing aids and cochlear implants for people with hearing disability. While speech is generally considered as a non-stationary signal over segment lengths longer than 20–30 ms, the perceptual stability of human auditory system motivates the need for an invariant representation of speech over long segment lengths. Computer modelling shows that STFT coefficients of speech with high-frequency resolution fit reasonably accurately to Laplace distribution (LD). Parameters of the corresponding LD are estimated using maximum-likelihood estimation. Cramer–Rao bound for the estimated parameters and root mean square error for the fitted distribution confirm the validity of the fitted distribution.