A Sequential Partial Optimization Algorithm for Design of Near Linear‐Phase IIR Digital Differentiators

Abstract

The linear phase is a major characteristic of digital differentiators in many signal processing applications. This study presents a sequential partial optimization method for designing a fullband infinite impulse response digital differentiator with a near linear phase. To achieve a near linear phase, the group delay is treated as an optimization variable, and the maximum phase error is minimized within a constrained domain. During each iteration of the algorithm, in addition to the whole numerator and group delay, only one secondorder denominator factor is optimized. The necessary and sufficient stability triangles are applied to insure the stability of the differentiators, and the Gauss-Newton strategy is used to handle the nonconvexity of the design problems. Design examples show that the proposed method outperforms several state-of-the-art methods in terms of the maximum phase deviation from the desired linear phase.