The choice between delta and shift operators for low-precision data representation

Abstract

Low-precision data types for embedded applications reduce the power consumption and enhance the price-performance ratio. Inconsistence between the specified accuracy of a designed filter or controller and an imprecise data type can be overcome using the δ-operator, an alternative to the traditional discrete-time z-operator. Though in many cases it significantly increases accuracy, sometimes it shows no advantage over the shift operator. So the problem of choice between delta and shift operator arises. Therefore, a study on δ-operator applicability bounds is needed to solve this problem and provide δ-operator efficient practical use. In this paper we introduce a concept of the δ-operator applicability criterion. The discrete system implementation technique with discrete-time operator choice is given for the low-precision machine arithmetic.