THEORY OF THE OPTIMUM APPROXIMATION OF MULTI-INPUT MULTI-OUTPUT FILTER BANKS AND TRANS-MULTIPLEXERS

摘要

We consider a one-dimensional multi-input multi-output system composed of given analysis-filter matrices, given sampler matrices and FIR interpolation-filter matrices to be optimized, respectively. We assume that the input-signal vector of this system is contained in a certain given set of input-signal vectors. The presented approximation minimizes any upper-limit measure of error compared to any other linear or nonlinear approximation using same sample values, simultaneously. Similar problem is treated in [8], In this paper, changing the definition of the measure of upper-limit error used in [8], we can eliminate the restriction of the kernel-function contained in [8] and derive more general one-dimensional vector signal approximation. Application to trans-multiplexers of vector signals is shown also.