Fast Deconvolution of Multi-Channel Systems using Regularisation by Ole Kirkeby, Philip A. Nelson, Hareo Hamada*, and Felipe Orduna-Bustamante # Institute of Sound & Vibration Research, Southampton University, SO17 1BJ, UK *Department of Electrical and Communications Engineering, Tokyo Denki University, Tokyo 101, Japan #Seccion de Acoustica, Centro de Instrumentos, UNAM, Circuito Exterior CU, Mexico DF A very fast FFT-based deconvolution method, which combines the well-known principles of least squares optimisation and regularisation, can be used for inverting systems comprising any number of inputs and outputs. The method was developed for the purpose of designing digital filters for multi-channel sound reproduction. It is typically several hundred times faster than a conventional steepest descent algorithm implemented in the time domain. A matrix of causal inverse FIR (finite impulse response) filters is calculated by optimising the performance of the filters at a large number of discrete frequencies. Consequently, this deconvolution method is useful only when it is feasible in practice to use relatively long inverse filters. The circular convolution effect in the time domain is controlled by zeroth-order regularisation of the inversion problem. It is necessary to set the regularisation parameter β to an appropriate value, but the exact value of β is usually not critical. For single-channel systems, a reliable numerical method for determining β without the need for subjective assessment is given. The deconvolution method is based on the analysis of a matrix of exact least squares inverse filters. The positions of the poles of those filters are shown to be particularly important. EDICS code: SA 2.3