Extension of the concept of multi-legged-type signals to the optimum multi- dimensional running approximation of multi-dimensional band-limited signals

摘要

The minimization of approximation errors in a FIR multi-dimensional filter bank for hand-limited signals is the important problem of multi-dimensional signal processing. In this paper, we consider the interpolation approximation that is modeled as a certain multi-dimensional FIR, filter bank. Firstly, we introduce the known optimum approximation of multi-dimensional signals in FIR, filter banks using a finite number of sample values. Secondly, we explain briefly a new concept of multi-legged-type signal that is a combined-signal of many one-dimensional band-limited signals. Backbone of this multi-legged-type signal is constituted with a set of small separable segments of the above one-dimensional signals that are determined by the proposed running approximation. Thirdly, we extend this concept to multi-dimensional hyper signal spa.ee. Based on this concept, we present an approximation method of the extended multi-dimensional multi-legged-type signals and we prove that this approximation in the hyper domain is the optimum. Finally, we define measures of error that become the proposed measures of error in the position of the backbone made by the corresponding multi-dimensional running approximation and become small about the other errors. Based on these measures of error, we prove that the presented multi-dimensional optimum approximation minimizes various continuous worst-case measures of the running approximation error at the same time.