Optimal Design of Nonlinear-Phase FIR Filters With Prescribed Phase Error

• Published in: IEEE transactions on signal processing Vol. 57; no. 9; pp. 3399 - 3410
• Main Author: Xiaoping Lai, Xiaoping Lai
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Applied sciences; Approximation; Approximation error; Chebyshev approximation; Constrained Chebyshev approximation; constrained least squares; Constraints; Delay; Detection, estimation, filtering, equalization, prediction; Error correction; Errors; Exact sciences and technology; Finite impulse response filter; FIR filters; Function approximation; Information, signal and communications theory; Least squares approximation; Least squares method; Miscellaneous; nonlinear phase; Optimization; Passband; Phase error; Quadratic programming; semi-infinite quadratic programming; Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; Performance evaluation; Least squares problem; Non linear filter; Error function; Semi infinite programming; Two dimensional model; Quadratic programming; Algorithm; Optimal design; FIR filters; constrained least squares; Digital filter; Simulation; Least squares method; semi-infinite quadratic programming; Optimal solution; nonlinear phase; Chebyshev approximation; Signal processing; Approximation error; Phase filter; Finite impulse response filter; Constrained Chebyshev approximation; Group delay
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2021639

Constrained least-squares design and constrained Chebyshev design of one- and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-definite quadratic programming approach. In order to obtain unique optimal solutions, we propose to impose constraints on the complex approximation error and the phase error. By introducing a sigmoid phase-error constraint bound function, the group-delay error can be greatly reduced. A Goldfarb-Idnani based algorithm is presented to solve the semi-infinite positive-definite quadratic program resulting from the constrained least-squares design problem, and then applied after some modifications to the constrained Chebyshev design problem, which is proved in this paper to be equivalent also to a semi-infinite positive-definite quadratic program. Through design examples, the proposed method is compared with several existing methods. Simulation results demonstrate the effectiveness and efficiency of the proposed method.