Blind deconvolution applied to acoustical systems identification with supporting experimental results

Many acoustical applications require the analysis of a signal that is corrupted by an unknown filtering function. Examples arise in the areas of noise or vibration control, room acoustics, structural vibration analysis, and speech processing. Here, the observed signal can be modeled as the convolution of the desired signal with an unknown system impulse response. Blind deconvolution refers to the process of learning the inverse of this unknown impulse response and applying it to the observed signal to remove the filtering effects. Unlike classical deconvolution, which requires prior knowledge of the impulse response, blind deconvolution requires only reasonable prior estimates of the input signal's statistics. The significant contribution of this work lies in experimental verification of a blind deconvolution algorithm in the context of acoustical system identification. Previous experimental work concerning blind deconvolution in acoustics has been minimal, as previous literature concerning blind deconvolution uses computer simulated data. This paper examines experiments involving three classical acoustic systems: driven pipe, driven pipe with open side branch, and driven pipe with Helmholtz resonator side branch. Experimental results confirm that the deconvolution algorithm learns these systems' inverse impulse responses, and that application of these learned inverses removes the effects of the filters.