Disclosed herein are systems and methods for removing reverberation from signals. The systems and methods can be applicable to audio signals, for example, to voice, musical instrument sounds, and the like. Signals such as the vowel sounds in speech and the sustained portions of many musical instrument sounds can be composed of a fundamental frequency component and a series of harmonically related overtones. The systems and methods can exploit the intrinsically high degree of mutual correlation among the overtones. When such signals are passed through a reverberant channel, the degree of mutual correlation among the partials can be reduced. An inverse channel filter for the removal of reverberation can be found by employing an adaptive filter technique that maximizes the cross-correlation among signal overtones.