Design of allpass filters with specified degrees of flatness and equiripple phase responses

This paper proposes a new method for designing allpass filters having the specified degrees of flatness at the specified frequency point(s) and equiripple phase responses in the approximation band(s). First, a system of linear equations are derived from the flatness conditions. Then, the Remez exchange algorithm is used to approximate the equiripple phase responses in the approximation band(s). By incorporating the linear equations from the flatness conditions into the equiripple approximation, the design problem is formulated as a generalized eigenvalue problem. Therefore, we can solve the eigenvalue problem to obtain the filter coefficients, which have the equiripple phase response and satisfy the specified degrees of flatness simultaneously. Furthermore, a class of IIR filters composed of allpass filters are introduced as one of its applications, and it is shown that IIR filters with flat passband (or stopband) and equiripple stopband (or passband) can be designed by using the proposed method. Finally, some examples are presented to demonstrate the effectiveness of the proposed design method.

[1]  C. Sidney Burrus,et al.  Generalized digital Butterworth filter design , 1998, IEEE Trans. Signal Process..

[2]  R. Hegde,et al.  Magnitude approximation of digital filters with specified degrees of flatness and constant group delay characteristics , 1998 .

[3]  C. Burrus,et al.  Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands , 1996 .

[4]  P. P. Vaidyanathan.  Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands , 1985 .

[5]  Unto K. Laine,et al.  Splitting the Unit Delay - Tools for fractional delay filter design , 1996 .

[6]  Sidney Darlington.  Filters with Chebyshev stopbands, flat passbands, and impulse responses of finite duration , 1978 .

[7]  W. Ivan,et al.  Lowpass Filters Realizable as Allpass Sums : Design via a New FlatDelay Filter , 1999 .

[8]  A. Lacroix,et al.  Magnitude and Delay Approximation of 1-D and 2-D Digital Filters , 1999 .

[9]  J. Thiran.  Recursive digital filters with maximally flat group delay , 1971 .

[10]  Xi Zhang,et al.  Design of IIR digital filters based on eigenvalue problem , 1996, IEEE Trans. Signal Process..

[11]  Xi Zhang,et al.  Design of IIR digital allpass filters based on eigenvalue problem , 1999, IEEE Trans. Signal Process..

[12]  Markus Lang,et al.  Allpass filter design and applications , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[13]  Chien-Cheng Tseng.  Design of IIR digital allpass filters using least pth phase error criterion , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[14]  S. Mitra,et al.  Handbook for Digital Signal Processing , 1993 .

[15]  P. Vaidyanathan,et al.  The digital all-pass filter: a versatile signal processing building block , 1988, Proc. IEEE.