Audio Source Separation and Speech Enhancement

3Acoustics: Spatial Properties

Emmanuel Vincent Sharon Gannot and Tuomas Virtanen

In Chapter 2, we presented the spectral properties of sound sources which can be exploited for the separation or enhancement of single‐channel signals. In multichannel scenarios, the fact that the acoustic scene is observed from different positions in space can also be exploited. In this chapter, we recall basic elements of acoustics and sound engineering, and use them to model multichannel mixtures.

We consider the relationship between a source signal and its spatial image in a given channel in Section 3.1, and examine how it translates in the case of microphone recordings or artificial mixtures in Sections 3.2 and 3.3, respectively. We then introduce several possible models in Section 3.4. We summarize the main concepts and provide links to other chapters and more advanced topics in Section 3.5.

3.1 Formalization of the Mixing Process

3.1.1 General Mixing Model

Sturmel et al. (2012) proposed the following general two‐stage model for audio mixtures. In the first stage, each single‐channel point source signal is transformed into an multichannel source spatial image signal by means of a possibly nonlinear spatialization ...