The optimum discrete running approximation of multidimensional time-limited signals
Yuichi Kida, Takuro Kida · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
In this paper, we present an integrated discussion of the space-limited but approximately band-limited ndimensional running discrete approximation that minimizes various continuous worst-case measures of error, simultaneously. Firstly, we introduce the optimum approximation using a fixed finite number of sample values and a running approximation that scans the sample values along the time-axis. Secondly, we derive another filter bank having both the set of extended number of transmission paths and a cutoff frequency over the actual Nyquist frequency. Thirdly, we obtain a continuous space-limited n-dimensional interpolation functions satisfying condition called extended discrete orthogonality. Finally, we derive a set of signals and discrete FIR filter bank that satisfy two conditions of the optimum approximation.