8 - Deconvolution and Inverse Filters

Abstract

Sound field control used in sound image projection for virtual reality technology requires equalization of the transfer functions (TF) including both magnitude and phase of the acoustic systems. This equalization is called inverse filtering or deconvolution, which is a key technology for dereverberation of reverberant speech signals or source waveform recovery for machine diagnostics. The chapter describes fundamentals of inverse filtering for acoustic TFs. It also discusses causality and stability of inverse filters, analytic signals, minimum-phase and all-pass decomposition, cepstrum, inverse filtering for minimum-phase components, and phase equalization. It explains the fundamentals of cepstrum processing and inverse filtering of continuous function forms are used for expressions with numerical examples. Inverse filtering is magnitude and phase equalization for the TF that describes signal transmission in an acoustic system. Thus, inverse filtering is an important technology in acoustic signal processing such as sound image projection and waveform recovery. The TF decomposition into the minimum-phase and all-pass components is important for producing an inverse filter as only the minimum-phase TF has a causal inverse filter. Taking the minimum-phase components, one can get a causal filter for a sound image projection system that preserves all the binaural information. The only information that is lost by disregarding the all-pass part is the monaural phase information.