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.
Bibliographic reference. Hershey, John R. / Olsen, Peder / Rennie, Steven J. (2010): "Signal interaction and the devil function", In INTERSPEECH-2010, 334-337.