Source Separation as a Multichannel Linear Filtering Problem

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 3)

The physical phenomena implied in multichannel speech processing include speech production at the vocal strings, sound propagation from the sound source to the microphone membrane, and analog-to-digital conversion of the signal. Instead of taking the complexity of these various phenomena into account, the acoustic signal processing algorithms studied in this book are based on the simplified model of a linear acoustic mixing.

This chapter explains this simplified model and is organized as follows: Section 2.1 describes the acoustic environment from the physical point of view and gives a mathematical formulation of the linear acoustic mixing model. In Sect. 2.2, the multichannel separation filters are presented for single and mul tiple outputs systems. The least-mean square (LMS) algorithm and a simple blind source separation (BSS) algorithm are briefly introduced to exemplify multichannel adaptive algorithms. The spatial response is introduced as a tool to interpret the separation filters spatially. In Sect. 2.3, we examine how the separation may be achieved and a lower bound on the length of the separation filters is derived. Finally, Sect. 2.4 defines the performance measures that will be used throughout the next chapters.


MIMO System Source Separation Blind Source Separation Spatial Response Microphone Array 
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© Springer Science+Business Media, LLC 2009

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