Audio Source Separation and Speech Enhancement

10Spatial Filtering

Shmulik Markovich‐Golan Walter Kellermann and Sharon Gannot

This chapter is dedicated to spatial filtering with applications to noise reduction and interference cancellation. Spatial filtering should be understood here as the application of linear, often time‐varying, filters to a multichannel signal acquired by microphones which are spatially distributed in the physical space (reverberant enclosures in the context of audio processing). The spatial diversity of the microphone arrangement allows for a spatially selective processing of the sound field. The term “beamformer” was historically used for a special class of spatial filtering system which directs a beam of high sensitivity to a certain region in space (or towards a certain direction) relative to the microphone arrangement. With the introduction of more complex propagation regimes that take reverberation into account, the term became more general. In the following, we use the term “beamformer” for all multiple‐input single‐output systems that produce a single output signal by combining a set of filtered microphone signals. Equivalently, the spatial filtering effect (not the optimization criteria for its design) by linear multiple‐input multiple‐output systems can be understood as the superposition of multiple beamformers. The output of the beamformer comprises an enhanced desired signal (or a combination of enhanced sources, e.g. a desired conversation) with (hopefully negligible) residual noise and competing ...