DAFX: Digital Audio Effects, Second Edition

14.3 Source Separation from Single-channel Signals

Separation of sources from single-channel (monophonic) mixtures is particularly challenging. If we have two or more microphones, we have seen earlier in this chapter that we can use information on relative amplitudes or relative time delays to identify the sources and to help us perform the separation. But with only one microphone, this information is not available. Instead, we must use information about the structure of the source signals to identify and separate the different components.

For example, one popular approach to the single-channel source separation problem is to use non-negative matrix factorization (NMF) of the Short Time Fourier Transform (STFT) power spectrogram of the audio signal. This method attempts to identify consistent spectral patterns in the different source signals, allowing these patterns to be associated with the different sources, then allowing separation of the audio signals. As well as NMF, we shall see that methods based on sinusoidal modeling and probabilistic modeling have also been proposed to tackle this difficult problem.

14.3.1 Source Separation Using Non-negative Matrix Factorization

Suppose that our mixture signal is composed of a weighted mixture of simple source objects, each with a fixed power spectrum , and where the relative energy of the pth object in the nth frame is given by spn ≥ ...