Derivation of Positive Realness Constraint with Specified Maximum Pole Radius and its Application to Design of Low-pass Digital Differentiators

Abstract

We present derivation of a new positive realness constraint of denominator polynomial. The positive realness constraint constrains the condition of specified maximum pole radius. Using the constraint to the design of infinite impulse response (IIR) digital filters, we can not only get a robust stable filter but also reduce the peak errors in the transition zone. Also, we formulate the design problem of low-pass differentiators, which is a class of digital filters, without frequency sampling. Incorporating the positive realness constraints we derived with the design problem of low-pass differentiators, the design problem can be expressed in a constrained quadratic programming problem. Finally, we show several examples to demonstrate the effectiveness of the proposed method.