An adaptive filter based on singular‐value decomposition of input signal correlation matrix

Abstract

AbstractAlthough various algorithms have been proposed for updating the filter coefficients of adaptive filters, problems still remain concerning their convergence speed and the accuracy of filter coefficients after the convergence. to solve these problems, this paper proposes an adaptive algorithm in which filter coefficients are obtained by solving a normal equation (for the optimized filter coefficients or the Wiener‐Hopf equation using eigenvalues of the input‐signal correlation matrix. If there are small eigenvalues in the input‐signal correlation matrix, they are assumed to be zero so that the filter coefficients are calculated by using a generalized inverse matrix. This prevents the increase of errors which occurs when the input is a correlative smooth signal. the proposed method matches nonsteady‐state signals, since the eigenvalues are successively calculated using the rank‐one‐modification method.The characteristics of the proposed adaptive filter were investigated, and a computer simulation of the filter as a noise canceller was carried out. the results show that the characteristics of the filter are superior to those of filters using conventional algorithms, although the amount of computation increases considerably.