Signal interaction and the devil function

It is common in signal processing to model signals in the log power spectrum domain. In this domain, when multiple signals are present, they combine in a nonlinear way. If the phases of the signals are independent, then we can analyze the interaction in terms of a probability density we call the “devil function,” after its treacherous form. This paper derives an analytical expression for the devil function, and discusses its properties with respect to model-based signal enhancement. Exact inference in this problem requires integrals involving the devil function that are intractable. Previous methods have used approximations to derive closed-form solutions. However it is unknown how these approximations differ from the true interaction function in terms of performance. We propose Monte-Carlo methods for approximating the required integrals. Tests are conducted on a speech separation and recognition problem to compare these methods with past approximations.