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Design of Linear Phase IIR Digital Filters Based on Eigenvalue Problem
Xi ZHANG Hiroshi IWAKURA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1996/04/25
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
IIR digital filter, linear phase filter, eigenvalue problem, approximation theory,
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It is known that an anticausal IIR filter can be realized in real time by using the time reversed section technique. When combined with a casual IIR filter, the overall transfer function can yield exact linear phase characteristic in theory. This paper presents a new method for designing complex IIR digital filters with exact linear phase. The design problem of IIR filters with exact linear phase can be reduced to magnitude-only filter design. The proposed procedure is based on the formulation of an eigenvalue problem by using Remez exchange algorithm. By solving the eigenvalue problem to compute the real maximum eigenvalue, the solution of the rational interpolation problem can be achieved. Therefore, the optimal filter coefficients are easily obtained through a few iterations. The proposed design algorithm not only retains the speed inherent in Remez exchange algorithm, but also Simplifies the interpolation step because is has been reduced to the computation of the real maximum eigenvalue. Several examples are presented to demonstrate the effectiveness of the proposed method.