Minimax Phase Error Design of IIR Digital Filters With Prescribed Magnitude and Phase Responses

• Published in: IEEE transactions on signal processing Vol. 60; no. 2; pp. 980 - 986
• Main Authors: Lai, Xiaoping, Lin, Zhiping
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Detection, estimation, filtering, equalization, prediction; Digital filters; Errors; Exact sciences and technology; Finite impulse response filter; Flexibility; Frequency response; IIR digital filters; IIR filters; Impulse response; Information, signal and communications theory; Least squares method; minimax phase error design; nonconvex constraints; Passband; Phase error; sequential constrained least-squares; Signal and communications theory; Signal, noise; Solids; Strategy; Telecommunications and information theory; Vectors; Performance evaluation; Infinite impulse response filter; Flexibility; Convex programming; Digital filter; nonconvex constraints; Least squares method; minimax phase error design; Minimax method; Signal processing; sequential constrained least-squares; Frequency response; IIR digital filters
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2175389

Infinite impulse response (IIR) digital filters with prescribed magnitude and phase responses have been used in many applications. To approximate the prescribed magnitude and phase responses, we propose a new approach to the design of general IIR filters by minimizing the maximum phase error subject to a prescribed or simultaneously minimized maximum magnitude error, where the phase error and magnitude error are controlled by two elliptic constraints respectively with major and minor axes along the desired frequency response. The sequential constrained least-squares method and Levy-Sanathanan-Koerner strategy are used to convert the nonconvex constraints into convex ones, resulting in a series of convex optimization subproblems. Design examples and comparisons with recent methods demonstrate the flexibility and effectiveness of the proposed methods.