Design of recursive differentiators using quadratic programming

A method for the design of first and higher-degree recursive differentiators with constant group-delay characteristics using a least-squares approach is presented. In this method, a mean-square error based on the difference between the desired and actual frequency response is formulated in a quadratic form. Quadratic programming is employed wherein the constraint on stability is accommodated to design stable differentiators. Our method is compared with the linear programming (LP) approach in terms of the computational complexity and the variation of magnitude and group-delay errors with frequency. It is shown that the differentiators designed using our method have a much lower computational complexity and smaller variation of the magnitude and group-delay error with frequency than those designed using the LP approach.<<ETX>>

[1]  A. Antoniou,et al.  Design of digital differentiators satisfying prescribed specifications using optimisation techniques , 1991 .

[2]  Graham A. Jullien,et al.  A linear programming approach to recursive digital filter design with linear phase , 1982 .

[3]  Lawrence R. Rabiner,et al.  The design of wide-band recursive and nonrecursive digital differentiators , 1970 .

[4]  Balbir Kumar,et al.  Design of efficient second and higher order FIR digital differentiators for low frequencies , 1990 .

[5]  Pei Soo-Chang,et al.  Design of FIR Hilbert transformers and differentiators by eigenfilter , 1988 .

[6]  S. C. Dutta Roy,et al.  Design of digital differentiators for low frequencies , 1988 .

[7]  Andreas Antoniou,et al.  Design of digital differentiators satisfying prescribed specifications using optimization techniques , 1989, IEEE International Symposium on Circuits and Systems,.

[8]  S. C. Dutta Roy,et al.  On the design of efficient second and higher degree FIR digital differentiators at the frequency π/(any integer) , 1992, Signal Process..

[9]  Balbir Kumar,et al.  Maximally linear FIR digital differentiators for high frequencies , 1989 .

[10]  Ravi P. Ramachandran,et al.  Least-squares design of higher order nonrecursive differentiators , 1994, IEEE Trans. Signal Process..

[11]  Andreas Antoniou,et al.  Design of digital differentiators satisfying prescribed specifications , 1980 .

[12]  L. Rabiner,et al.  FIR digital filter design techniques using weighted Chebyshev approximation , 1975, Proceedings of the IEEE.

[13]  Soo-Chang Pei,et al.  Eigenfilter design of higher-order digital differentiators , 1989, IEEE Trans. Acoust. Speech Signal Process..

[14]  S. D. Roy,et al.  Maximally linear FIR digital differentiators for midband frequencies , 1989 .

[15]  Enders A. Robinson,et al.  Statistical Communication and Detection , 1967 .

[16]  Andreas Antoniou,et al.  Improved design method for kaiser differentiators and comparison with equiripple method , 1981 .

[17]  S. D. Roy,et al.  Coefficients of maximally linear, FIR digital differentiators for low frequencies , 1988 .

[18]  Craig A. Rahenkamp,et al.  Modifications to the McClellan, Parks, and Rabiner computer program for designing higher order differentiating FIR filters , 1986, IEEE Trans. Acoust. Speech Signal Process..