Instantaneous Blind Audio Source Separation Using Characteristic Function of Heavy-Tailed Distibutions

Blind audio source separation (BASS) methods separate combined audio signals up to unknown scaling and ordering factors. The present study proposes an interesting approach by assigning symmetric alpha-stable $(\text{S}\alpha \text{S})$ distributions to sources. Since $\text{S}\alpha \text{S}$ distributions can better model audio signal due to their heavier tails, our method outperformed other well-renowned algorithms. The main drawback of $\text{S}\alpha \text{S}$ distributions is the lack of closed-form expression for its density function, apart from some exceptional cases. But promising fact is that its characteristic function has closed-formed relation. In this study, discrete formula of characteristic function, defined based on spectral measure, was used to tackle BASS. Our signals were combined linearly and instantaneously in each sensor, number of sources and sensors were equal, i.e., the case was so-called determined case. While our method can be implemented in determined case, its efficiency has been proven even in mild underdetermined cases. The solution devised for BASS problem presumes that sources are independent and identically distributed (i.i.d.), which is not far from real condition.