On pole-zero patterns of non-negative impulse response discrete-time systems with complex poles and zeros

Abstract

This paper presents a new set of sufficient conditions on complex poles and zeros to ensure the non-negativity of the impulse response of an arbitrary-order discrete-time system. Different from previous work, this set of sufficient conditions expose an interesting geometric pole-zero pattern — poles and zeros are evenly distributed on different concentric circles centered at origin. By controlling the number of poles/zeros on each circle and using pole-zero cancellation to de-regularize the pole-zero distribution, the class of pole-zero patterns known to exhibit a non-negative impulse response (NNIR) are significantly expanded. And this set of sufficient conditions can be easily employed for designing NNIR filters.