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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Restricted range approximation and its application to digital filter design
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by James T. Lewis PDF
Math. Comp. 29 (1975), 522-539 Request permission

Abstract:

The multiple exchange algorithm for restricted range approximation is discussed. Efficient formulas are derived for the numerical implementation of the method. Discretization effects are analyzed mathematically. The method is applied to a certain problem arising in digital filter design.
References
    M. C. BUDGE, R. K. CAVIN & D. R. GIMLIN, "Non-recursive filter design via best restricted approximations," Manuscript.
  • E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
  • D. R. Gimlin, R. K. Cavin III, and M. C. Budge Jr., A multiple exchange algorithm for calculation of best restricted approximations, SIAM J. Numer. Anal. 11 (1974), 219–231. MR 373226, DOI 10.1137/0711021
  • H. D. HELMS, "Digital filters with equiripple or minimax responses," IEEE Trans. Audio and Electroacoust., Vol. AU-19, pp. 87-93, March 1971. H. S. HERSEY, D. W. TUFTS & J. T. LEWIS, "Interactive minimax design of linear-phase nonrecursive digital filters subject to upper and lower function constraints," IEEE Trans. Audio and Electroacoust., pp. 171-173, June 1972. F. K. KUO & J. F. KAISER, System Analysis by Digital Computer, Chapter 7, Wiley, New York, 1966.
  • James T. Lewis, Computation of best monotone approximations, Math. Comp. 26 (1972), 737–747. MR 329199, DOI 10.1090/S0025-5718-1972-0329199-3
  • T. W. PARKS & J. H. McCLELLAN, "Chebyshev approximation for nonrecursive digital filters with linear phase," IEEE Trans. Circuit Theory, vol. CT-19, no. 2, pp. 189-194, March 1972. C. M. RADER & B. GOLD, Digital Processing of Signals, McGraw-Hill, New York, 1969.
  • John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
  • G. D. Taylor, Approximation by functions having restricted ranges. III, J. Math. Anal. Appl. 27 (1969), 241–248. MR 257611, DOI 10.1016/0022-247X(69)90045-6
  • G. D. Taylor and M. J. Winter, Calculation of best restricted approximations, SIAM J. Numer. Anal. 7 (1970), 248–255. MR 269082, DOI 10.1137/0707017
  • D. W. TUFTS, J. T. LEWIS & H. S. HERSEY, Interactive Minimax Design of Nonrecursive Digital Filters, Report EE 4044/1, Dept. of Electrical Engineering, Univ. of Rhode Island, Kingston, R. I., October 1972.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 522-539
  • MSC: Primary 65D15; Secondary 94A05
  • DOI: https://doi.org/10.1090/S0025-5718-1975-0381245-X
  • MathSciNet review: 0381245