Methods and systems for non-negative hidden Markov modeling of signals are described. For example, techniques disclosed herein may be applied to signals emitted by one or more sources. In some embodiments, methods and systems may enable the separation of a signal's various components. As such, the systems and methods disclosed herein may find a wide variety of applications. In audio-related fields, for example, these techniques may be useful in music recording and processing, source extraction, noise reduction, teaching, automatic transcription, electronic games, audio search and retrieval, and many other applications.