Probabilistic Modeling of Speech in Spectral Domain using Maximum Likelihood Estimation

The performance of many speech processing algorithms depends on modeling speech signals using appropriate probability distributions. Various distributions such as the Gamma distribution, Gaussian distribution, Generalized Gaussian distribution, Laplace distribution as well as multivariate Gaussian and Laplace distributions have been proposed in the literature to model different segment lengths of speech, typically below 200 ms in different domains. In this paper, we attempted to fit Laplace and Gaussian distributions to obtain a statistical model of speech short-time Fourier transform coefficients with high spectral resolution (segment length >500 ms) and low spectral resolution (segment length <10 ms). Distribution fitting of Laplace and Gaussian distributions was performed using maximum-likelihood estimation. It was found that speech short-time Fourier transform coefficients with high spectral resolution can be modeled using Laplace distribution. For low spectral resolution, neither the Laplace nor Gaussian distribution provided a good fit. Spectral domain modeling of speech with different depths of spectral resolution is useful in understanding the perceptual stability of hearing which is necessary for the design of digital hearing aids.

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