Design of Chebyshev-Type IIR Filters with Approximately Linear Phase Characteristics

Digital filters with a linear phase characteristic are needed in many applications for signal processing. In this paper, design of a Chebyshev-type IIR filter with approximate linear phase characteristics in the passband is described. First, it is shown that a flat stopband can easily be realized by placing multiple zeros at the specified frequency points in the stopband. Next, the complex Remez exchange algorithm is applied to the passband so that the filter design problem is formulated as an eigenvalue problem. Hence, by solving the eigenvalue problem, the filter coefficients can be derived easily. Further, by means of iterative calculations, an equiripple characteristic of the error function in the passband is obtained. Finally, it is shown that a reverse Chebyshev-type IIR filter with an approximate linear phase characteristic can also be obtained by parallel connection of the proposed Chebyshev-type filter and a delay line. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(2): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10133