Elliptic functions for filter design

This paper offers a simple description of the elementary properties of the Jacobian elliptic functions and of the Landen transformation, which connects them with the circular and hyperbolic functions and thereby provides one of the most accurate methods of evaluating elliptic functions. The use of elliptic functions in creating equal-ripple lowpass filters is explained and their numerical evaluation is illustrated by means of an example. A Fortran program for effecting the design is included and a faster and more accurate replacement for the Matlab program ELLIPAP is given.

[1]  A. Antoniou.  Digital Filters: Analysis, Design and Applications , 2018 .

[2]  Miroslav D. Lutovac,et al.  Minimum stopband attenuation of Cauer filters without elliptic functions and integrals , 1993 .

[3]  M. Lutovac,et al.  Comments on "The effects of lower Q values on the filters having equal ripples in passband" by H. Kim , 1993 .

[4]  M. Lutovac,et al.  Algebraic design of some lower-order elliptic filters , 1993 .

[5]  M. Lutovac,et al.  A simplified design of some Cauer filters without Jacobian elliptic functions , 1992 .

[6]  D. Baez-López,et al.  Computation of even-order elliptic filter functions , 1986 .

[7]  Sidney Darlington,et al.  Simple algorithms for elliptic filters and generalizations thereof , 1978 .

[8]  P. Amstutz,et al.  Elliptic approximation and elliptic filter design on small computers , 1978 .

[9]  Gabor C. Temes,et al.  Computational algorithm for the design of elliptic filters , 1972 .

[10]  H. Orchard,et al.  Computation of Elliptic Functions of Rational Fractions of a Quarterperiod , 1958 .

[11]  Alexander J. Grossman,et al.  Synthesis of Tchebycheff Parameter Symmetrical Filters , 1957, Proceedings of the IRE.

[12]  E. H. Neville,et al.  Jacobian Elliptic Functions , 1952, The Mathematical Gazette.

[13]  S. Darlington,et al.  Synthesis of Reactance 4-Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter Design , 1939 .

[14]  Lajos Gazsi,et al.  Explicit formulas for lattice wave digital filters , 1985 .