The Design of Nonrecursive Digital Filters via Convex Optimization

The advantages of optimization in filter design over strongly specialized methods based upon approximation theory are well known since some years, first of all in the area of constrained linear-phase filter design. Mainly finite linear optimization has been used which requires the discretization w.r.t. the frequency variable and, if necessary, the linearization of important nonlinear filter characteristics. The work here is founded on convex finite and semi-infinite optimization. The approach avoids the discretization step and thereby, in particular, enables the design of large filters on personal computers. Moreover, convex functions such as the magnitude response, magnitude of the complex approximation error, and some quadratic error functions can be used in their original form.

[1]  R. Reemtsen.  Design Problems for Nonrecursive Digital Filters I , 1997 .

[2]  Hans Wilhelm Schüßler.  Digitale Signalverarbeitung 1 , 1994 .

[3]  Kenneth Steiglitz,et al.  METEOR: a constraint-based FIR filter design program , 1992, IEEE Trans. Signal Process..

[4]  Peter Steffen,et al.  Some advanced topics in filter design , 1987 .

[5]  Alexander Potchinkov.  Design of optimal linear phase FIR filters by a semi-infinite programming technique , 1997, Signal Process..

[6]  S. Biyiksiz,et al.  Multirate digital signal processing , 1985, Proceedings of the IEEE.

[7]  Alexander Potchinkov,et al.  FIR filter design in the complex domain by a semi-infinite programming technique. I: The method , 1994 .

[8]  Rembert Reemtsen,et al.  Numerical Methods for Semi-Infinite Programming: A Survey , 1998 .

[9]  Klaus Preuss,et al.  On the design of FIR filters by complex Chebyshev approximation , 1989, IEEE Trans. Acoust. Speech Signal Process..

[10]  Kenneth Steiglitz,et al.  Design of FIR digital phase networks , 1980, ICASSP.

[11]  Kevin G. Christian,et al.  Design and characterization of optimal FIR filters with arbitrary phase , 1993, IEEE Trans. Signal Process..

[12]  Jennifer Adams,et al.  FIR digital filters with least-squares stopbands subject to peak-gain constraints , 1991 .

[13]  Thomas W. Parks,et al.  Design of FIR filters in the complex domain , 1987, IEEE Trans. Acoust. Speech Signal Process..

[14]  Guido M. Cortelazzo,et al.  Simultaneous design in both magnitude and group-delay of IIR and FIR filters based on multiple criterion optimization , 1984 .

[15]  Jae S. Lim,et al.  Advanced topics in signal processing , 1987 .

[16]  Alexander Potchinkov,et al.  The design of FIR filters in the complex plane by convex optimization , 1995, Signal Process..

[17]  L. Rabiner,et al.  A computer program for designing optimum FIR linear phase digital filters , 1973 .

[18]  J. McClellan,et al.  Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase , 1972 .

[19]  Alexander Potchinkov.  Entwurf minimalphasiger nichtrekursiver digitaler Filter mit Verfahren der nichtlinearen Optimierung , 1997 .

[20]  Joseph S. Rosko,et al.  Digital Simulation of Physical Systems , 1972 .

[21]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Keh-Shew Lu,et al.  DIGITAL FILTER DESIGN , 1973 .

[23]  Thomas W. Parks,et al.  Optimal design of FIR filters with the complex Chebyshev error criteria , 1995, IEEE Trans. Signal Process..

[24]  Fred J. Taylor,et al.  Digital Filter Design Handbook , 1983 .

[25]  Francis Grenez.  Design of linear or minimum-phase fir filters by constrained chebyshev approximation , 1983 .

[26]  Alexander Potchinkov,et al.  THE SIMULTANEOUS APPROXIMATION OF MAGNITUDE AND PHASE BY FIR DIGITAL FILTERS. II: METHODS AND EXAMPLES , 1997 .

[27]  Wen-Shyong Yu,et al.  An l/sub 1/-approximation based method for synthesizing FIR filters , 1992 .