A general MMSE joint detection and estimation of speech signal based on generalized gamma priors

In this paper, we present a comprehensive model for a simultaneous detection and estimation of Discrete Fourier Transform (DFT) coefficients of speech signals. Our proposed model suggests using a Generalized Gamma Probability Density Function (PDF) to represent the magnitudes of the DFT coefficients of speech signals. Classical probability density functions (PDFs), such as the Rayleigh PDF, are inadequate for accurately modeling speech signal. These models often rely on oversimplified assumptions about the statistical properties of speech signals. These assumptions limit their effectiveness in practical applications. Our study aims to derive a comprehensive simultaneous detection and estimation model based on the Generalized Gamma Distribution (GΓD). We employ the Minimum Mean Square Error (MMSE) estimator to the magnitudes of Discrete Fourier Transform (DFT) coefficients in the Short-Time Fourier Transform (STFT) domain. This approach allows us to effectively model the statistical properties of speech signals using GΓD. Our analyses demonstrate that adopting the GΓD framework can enhance the performance of speech signal detection and estimation in noisy environments, as evidenced by objective evaluation measures.