Log-Rayleigh Distribution: A Simple and Efficient Statistical Representation of Log-Spectral Coefficients

In this paper, we study the distribution of the log-modulus of a Gaussian complex random variable. In the circular case, it is a Log-Rayleigh (LR) variable, whose probability distribution function (pdf) depends on only one parameter. In the noncircular case, the pdf is more complicated, although we show that it can be adequately modeled by an LR pdf, for which the optimal fitting parameter is derived. These results can be used in any application using the log-modulus of discrete Fourier transform coefficients, e.g., for speech/audio signals, and suggest that a mixture of LR pdf kernels is preferable to more classical models such as mixtures of Gaussian kernels, which are more costly and less efficient