Stable IIR digital differentiator design using iterative quadratic programming approach

Abstract In this paper, we present an iterative quadratic programming approach to design stable IIR digital differentiator. At each iteration, the cost function is transformed into a quadratic form by treating the denominator polynomial obtained from the preceding iteration as a part of the weighting function, and the pole radii are constrained to lie in the unit circle by using the implications of Rouche's theorem. After solving the standard quadratic programming problem at each iteration, the design algorithm converges to a stable and truly weighted least-squares solution. Design examples demonstrate that our method provides a better design results than the conventional quadratic programming method.