THEORY OF THE OPTIMUM APPROXIMATION OF VECTOR SIGNALS BASED ON MULTI-INPUT MULTI OUTPUT FILTER BANKS

摘要

In this paper, we define a multi-input multi-output system composed of given analysis-filter matrices, given sampler matrices and interpolation-filter matrices to be optimized, respectively. It is assumed that input-signal vectors of this system are contained in a certain given set of input-signal vectors. Firstly, we define a new notation which expresses a kind of product between a vector and a matrix and, using this new notation, we show that the presented approximation satisfies a certain two conditions and prove that the presented approximation minimizes any upper-limit measure of error compared to any other linear or nonlinear approximation with same sample values, simultaneously.