Modeling the effects of dynamic range compression on signals in noise

Hearing aids use dynamic range compression (DRC), a form of automatic gain control, to make quiet sounds louder and loud sounds quieter. Compression can improve listening comfort, but it can also cause unwanted distortion in noisy environments. It has been widely reported that DRC performs poorly in noise, but there has been little mathematical analysis of these noise-induced distortion effects. This work introduces a mathematical model to study the behavior of DRC in noise. By making simplifying assumptions about the signal envelopes, we define an effective compression function that models the compression applied to one signal in the presence of another. Using the properties of concave functions, we prove results about DRC that have been previously observed experimentally: that the effective compression applied to each sound in a mixture is weaker than it would have been for the signal alone; that uncorrelated signal envelopes become negatively correlated when compressed as a mixture; and that compression can reduce the long-term signal-to-noise ratio in certain conditions. These theoretical results are supported by software experiments using recorded speech signals.