Design of nearly linear-phase recursive digital filters by constrained optimization

A methodology for the design of recursive digital filters having nearly linear phase response is proposed. The underlying design method is of the direct type whereby the filter is designed as a single block. The design problem is formulated as a cascade of filter sections where each section is represented by a biquadratic transfer function in the polar form. The design problem is then solved using a constrained Newton's method whereby the constraints assure the stability of the filter and control the step size in order to achieve fast convergence. Design examples demonstrate that, when compared to filters designed using existing state-of-the art methods, the proposed methodology yields filters having reduced order and/or improved performance.