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