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Restricted range approximation and its application to digital filter design


Author: James T. Lewis
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] M. C. BUDGE, R. K. CAVIN & D. R. GIMLIN, "Non-recursive filter design via best restricted approximations," Manuscript.
  • [2] E. W. CHENEY, Introduction to Approximation Theory, McGraw-Hill, New York, 1966. MR 36 #5568. MR 0222517 (36:5568)
  • [3] D. R. GIMLIN, R. K. CAVIN & M. C. BUDGE, "A multiple exchange algorithm for calculation of best restricted approximations," SIAM J. Numer. Anal., v. 11, 1974, pp. 219-231. MR 0373226 (51:9427)
  • [4] H. D. HELMS, "Digital filters with equiripple or minimax responses," IEEE Trans. Audio and Electroacoust., Vol. AU-19, pp. 87-93, March 1971.
  • [5] 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.
  • [6] F. K. KUO & J. F. KAISER, System Analysis by Digital Computer, Chapter 7, Wiley, New York, 1966.
  • [7] J. T. LEWIS, "Computation of best monotone approximations," Math. Comp., v. 26, 1972, pp. 737-747. MR 0329199 (48:7541)
  • [8] 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.
  • [9] C. M. RADER & B. GOLD, Digital Processing of Signals, McGraw-Hill, New York, 1969.
  • [10] J. R. RICE, The Approximation of Functions. Vol. 1: Linear Theory, Addison-Wesley, Reading, Mass., 1964. MR 29 #3795. MR 0166520 (29:3795)
  • [11] G. D. TAYLOR, "Approximation by functions having restricted ranges. III," J. Math. Anal. Appl., v. 27, 1969, pp. 241-248. MR 41 #2261. MR 0257611 (41:2261)
  • [12] G. D. TAYLOR & M. J. WINTER, "Calculation of best restricted approximations," SIAM J. Numer. Anal., v. 7, 1970, pp. 248-255. MR 42 #3978. MR 0269082 (42:3978)
  • [13] 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

DOI: https://doi.org/10.1090/S0025-5718-1975-0381245-X
Keywords: Approximation with restricted range, computation of best approximations, digital filter design
Article copyright: © Copyright 1975 American Mathematical Society

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