Design Methodology for Nearly Linear-Phase Recursive Digital Filters by Constrained Optimization

Abstract

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 unit. The design problem is formulated as a cascade of filter sections where each section is represented by a biquadratic transfer function either in the conventional polynomial form or in the polar form. The design problem is then solved using a constrained Newton's method whereby constraints are used to assure the stability of the filter, to control the step size in order to achieve fast convergence, and to eliminate a real-axis pole-migration problem that often interferes with the design process. Several design examples demonstrate that when compared with filters designed using existing state-of-the-art methods, the proposed methodology yields filters having reduced order and/or improved performance.

Design of nearly linear-phase recursive digital filters by using unconstrained least-pth minimax optimization

“…The filter obtained is compared with corresponding filters designed using the parameterization (PAM) and the constrained optimization method (COPM) in [5] and [14], respectively. The results obtained are summarized in Table III and the amplitude response and the passband relative group-delay deviation plots are illustrated in Fig.…”

“…4, the proposed method resulted in a reduced maximum passband ripple, maximum group-delay deviation, and group delay and also increased minimum stopband attenuation. The proposed method was found to be more efficient than the other two method requiring 69.6% and 13.2% of the computational effort required by the methods in [5] and [14], respectively. Table I.…”

“…A central issue in all the methods for the design of recursive digital filters by optimization is the issue of stability since an optimization Manuscript approach can easily yield an unstable filter that would be of no use. Many strategies have been explored to assure the stability of the filter, and each strategy has given rise to a corresponding methodology [5]- [14].…”

“…The new method achieves filter stability through the use of a parameterization scheme based on the so-called sigmoid function [16], [17] and it incorporates a mechanism by which an arbitrary prescribed stability margin can be achieved. The proposed method was used to design various lowpass filters and the filters obtained are compared with corresponding filters designed using the methods in [4], [5], [12], and [14]. The paper is organized as follows.…”

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

“…More recent methods typically involve designing IIR filters that simultaneously satisfy both the amplitude-and phase-response constraints, as it results in filters of lower order [5]- [14]. In [8], the frequency-response error is minimized under the constraint that the group-delay deviation is within a prescribed level, while in [5] the design problem is formulated as a cascade of filter sections where each section is represented by a biquadratic transfer function either in the conventional polynomial form or in the polar form and the design problem is solved using a constrained Newton method. An important advantage of this method is the nonrestrictive stability constraint that it uses coupled with the capability of controlling the maximum pole radius.…”