On the FIR Inversion of an Acoustical Convolutive Mixing System: Properties and Limitations

Abstract

In this paper we address the problem of Least-Squares (LS) optimal FIR inverse-filtering of an convolutive mixing system, given by a set of acoustic impulse responses (AIRs). The optimal filter is given by the LS-solution of a block-Toeplitz matrix equation, or equivalently by the time-domain Multi-Channel Wiener Filter. A condition for the minimum FIR filter length can be derived, depending on the number of sensors and sources and the AIR length, such that an exact FIR inverse exists, which perfectly separates and deconvolves all sources. In the general case, where an exact FIR solution does not exist, we discuss how SDR, SIR and SNR gains can be traded against each other. Results are shown for a set of AIRs, measured in an typical office room. Furthermore we present a method, which allows a time-domain shaping of the envelope of the global transfer function, reducing pre-echoes and reverberation.