Speech signal modeling using multivariate distributions

Abstract

Using a proper distribution function for speech signal or for its representations is of crucial importance in statisticalbased speech processing algorithms. Although the most commonly used probability density function (pdf) for speech signals is Gaussian, recent studies have shown the superiority of super-Gaussian pdfs. A large research effort has focused on the investigation of a univariate case of speech signal distribution; however, in this paper, we study the multivariate distributions of speech signal and its representations using the conventional distribution functions, e.g., multivariate Gaussian and multivariate Laplace, and the copula-based multivariate distributions as candidates. The copula-based technique is a powerful method in modeling non-Gaussian multivariate distributions with non-linear inter-dimensional dependency. The level of similarity between the candidate pdfs and the real speech pdf in different domains is evaluated using the energy goodness-of-fit test. In our evaluations, the best-fitted distributions for speech signal vectors with different lengths in various domains are determined. A similar experiment is performed for different classes of English phonemes (fricatives, nasals, stops, vowels, and semivowel/glides). The evaluation results demonstrate that the multivariate distribution of speech signals in different domains is mostly super-Gaussian, except for Mel-frequency cepstral coefficient. Also, the results confirm that the distribution of the different phoneme classes is better statistically modeled by a mixture of Gaussian and Laplace pdfs. The copula-based distributions provide better statistical modeling of vectors representing discrete Fourier transform (DFT) amplitude of speech vectors with a length shorter than 500 ms.

Estimation of the Probability Distribution of Spectral Fine Structure in the Speech Source

“…Though this result is hardly surprising, it is more specific than prior works such as [8,9,10], since we include the contribution of the speech production model and can evaluate phoneme groups separately.…”

“…Selection of the best probability distribution model is therefore important for the efficiency of the algorithms, whereby many have investigated the issue [8,9,10]. In general, Gaussian models and mixture models thereof are appealing due to their analytic and computational properties, but practice have shown that in many cases the Laplacian distribution is a more accurate model of many representations of speech signals.…”

An Expectation–Maximization-Based IVA Algorithm for Speech Source Separation Using Student’s t Mixture Model Based Source Priors

“…In the joint pdf of the Student's t distribution, the leptokurtic nature and the variance of distribution can be adjusted by tuning the degrees of freedom parameter ν [30]. When the ν parameter is set to a lower value, the tails of the distribution becomes heavier and if ν is increased to infinity, the Student's t distribution tends to a Gaussian distribution [19,20].…”

Log-Spectral Amplitude and Spectral Polarity Estimation in Short-Time Discrete Cosine Transform Domain

“…Motivated by the central limit theorem, the complex Gaussian model was used for both DFT clean speech and noise components. Later studies show that while noise components can be appropriately modeled by Gaussian distributions, clean speech components in the decorrelated domains are more accurately described by super-Gaussian distributions such as Laplacian (doublesided Exponential) [18], [21], [22]. Thus, employing a super-Gaussian speech prior instead of the Gaussian can improve the performance of MMSE STSA estimators [18], [22]- [24].…”

“…Later studies show that while noise components can be appropriately modeled by Gaussian distributions, clean speech components in the decorrelated domains are more accurately described by super-Gaussian distributions such as Laplacian (doublesided Exponential) [18], [21], [22]. Thus, employing a super-Gaussian speech prior instead of the Gaussian can improve the performance of MMSE STSA estimators [18], [22]- [24]. In particular, Hendriks et al [6] derived an MMSE LSA estimator under the assumption that the clean speech DFT amplitudes are following a one-sided chi distribution.…”