Calculating the jacobi elliptic functions to calculate the characteristics of cauer filter

Author(s):  V.P. Volchkov, Dr., Prof., Moscow Technical University of Communications and Informatics, Moscow, Russia, volchkovvalery@mail.ru

A.V. Miroshnichenko, Moscow Technical University of Communications and Informatics, Moscow, Russia, Mirosh.A.V@yandex.ru

Issue:  Volume 45, №2

Rubric:  Computer simulation history

Annotation:  The problem of calculation and analysis of elliptic filter (Cauer filter), which consists in calculating the Jacobi elliptic functions, used for mathematical approximation Cauer filter transfer function. Provides integral for determining the direct and inverse Jacobi elliptic functions that depend on two parameters u, k. For direct Jacobi elliptic functions were developed five algorithms of calculation: the arithmetic-geometric mean method with Landen's transformation, approximation using trigonometric and hyperbolic functions, Taylor series and Fourier series expansion. For inverse by u Jacobi elliptic functions analyzed four algorithms of calculation: the arithmetic-geometric mean method, Cotes formulas, Simpson's method and the Monte Carlo method. Discusses the problem of calculation the inverse by parameter k Jacobi el-liptic function. Offered possible solutions to this problem, among which a complete enumeration and at-tempt approximation through trigonometric and hyperbolic functions. Describes and compares the results obtained in different ways. Recommendations on the use of different methods of calculating the Jacobi elliptic functions in problems of synthesis and analysis of Cauer filters.

Keywords:  Cauer filter, Jacobi elliptic functions, the arithmetic-geometric mean method, Landen's trans-formation, Taylor series, Fourier series, Cotes formulas, Simpson's method, Monte Carlo method.

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