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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.

Optimal designs of finite impulse response (FIR) digital filters with prescribed magnitude and phase responses have found many applications in signal processing. To deal with the nonconvexity of the constraint region in the phase-error and magnitude-error constrained design, a new error constraint method based on a modified annulus sector (MAS) is proposed. With the new constraint method, the phase-error and magnitude-error constrained least squares, phase-error constrained minimax, and iterative reweighted phase-error constrained minimax designs of FIR filters are studied. Analyses and design examples demonstrate the higher accuracy of the MAS constraint and better filter performance by the constraint method than existing constraint methods. An application in the design of digital differentiators with flatness constraints is also provided.

New designs of infinite impulse response (IIR) wideband digital integrators of second-, third- and forth-order are presented in this paper. These new integrators are designed by a recently proposed magnitude constrained minimax phase-error method. In these designs, the maximum phase response error is minimized under some constraints that the maximum relative magnitude response error is below a prescribed level. Simulation results show that our proposed wideband IIR digital integrators have much smaller maximum phase response error and maximum relative magnitude error than existing wideband IIR digital integrators in the literature.

Magnitude-error and phase-error constrained optimal designs of finite impulse response (FIR) filters are nonconvex problems due to the nonconvexity of the lower-bound constraint of magnitude at any passband frequency point. In order to solve these problems, the nonconvex constraint region at an arbitrary passband frequency is usually approximated by a convex one. In this paper, a new convex constraint model is proposed. It approximates the nonconvex lower-bound magnitude constraint by a linear one while keeping the upper-bound magnitude and phase-error constraints unchanged. Design results demonstrate the effectiveness of the proposed constraint model and good performance of the designed filters.