Multichannel signal decorrelation using a new generalization of the prediction error filter

Abstract

In many multichannel adaptive active control systems the convergence speed is limited by the correlations between the reference signal channels. This paper describes a causal digital filter capable of reducing multiple channel correlated colored input data to an underlying set of uncorrelated unit variance white signals. This filter is the inverse of the spectral factorization matrix for this data set. The problem is approached in two steps. In the first step it is shown analytically that a single-point delay prediction error filter (PEF) will produce white output error data from multiple nonwhite inputs. The flaw in this process is that there is an inherent matrix of gains which scales and correlates the output channels. In the second step, a technique is presented to derive this matrix of gains from the spectral density matrix of the filter output and thus calculate the appropriate inverse filter. The output from this two-step process is uncorrelated, unit variance and white. The complete signal reduction algorithm is then demonstrated for multiple-channel simulated signals and is finally calculated and tested on correlated road noise data.