On the non-negative impulse response of continuous-time multi-dimensional systems

Abstract

This paper presents sufficient conditions on 1-D pole-zero patterns that exhibit a non-negative impulse response (NNIR) for several classes of multi-dimensional (m-D) hyper-planar filters in the continuous-time (C-T) domain. The results provide some intuitive ideas about 1-D to m-D variable substitutions that preserve the positivity/non-negativity property, and are useful for constructing m-D NNIR filters from 1-D prototypes.