A FAST CALCULATION METHOD OF THE OPTIMUM RUNNING INTERPOLATION OF VECTOR SIGNALS ON MULTI-DIMENSIONAL FIR FILTER BANKS

摘要

In this paper, we present the optimum interpolatory approximation of vector signals that is time-limited in wide interval in the time-domain and is band-limited approximately in the frequency-domain. Firstly, we provide a method of obtaining the optimum multi-dimensional interpolatory approximation for a certain measure of absolute error. Furthermore, we prove that the approximation minimizes various measure of approximation error, simultaneously. Secondly, we provide an interesting design method of multi-dimensional FIR filter bank. Thirdly, we present a fast calculation method to obtain the optimum interpolation functions based on a property of block Toeplitz matrices and multi-dimensional FFT.