Complex Chebyshev approximation for IIR digital filters based on eigenvalue problem

• Published in: IEEE transactions on circuits and systems. 2, Analog and digital signal processing Analog and digital signal processing, 2000-12, Vol.47 (12), p.1429-1436
• Main Authors: Xi Zhang, Suzuki, K., Yoshikawa, T.
• Format: Article
• Language: English
• Subjects: Algorithm design and analysis; Approximation algorithms; Chebyshev approximation; Design methodology; Digital filters; Eigenvalues and eigenfunctions; Finite impulse response filter; IIR filters; Interpolation; Signal processing algorithms
• ISSN: 1057-7130; 1558-125X
• DOI: 10.1109/82.899636

This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, and then the complex Chebyshev approximation is attained through a few iterations starting from a given initial guess. The proposed algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step. Some design examples are presented and compared with the conventional methods. It is shown that the results obtained by using the method proposed in this paper are better than those obtained by the conventional methods.