Synthesis of a Rational Filter in the Presence of Complete Alternance

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Synthesis of a Rational Filter in the Presence of Complete Alternance. / Malozemov, V.N.; Tamasyan, G.Sh.

In: Computational Mathematics and Mathematical Physics, Vol. 57, No. 6, 2017, p. 919–930.

Research output: Contribution to journal › Article › peer-review

Author

Malozemov, V.N. ; Tamasyan, G.Sh. / Synthesis of a Rational Filter in the Presence of Complete Alternance. In: Computational Mathematics and Mathematical Physics. 2017 ; Vol. 57, No. 6. pp. 919–930.

BibTeX

@article{d2c4b59253224c5abe780a8282cfaf0c,

title = "Synthesis of a Rational Filter in the Presence of Complete Alternance",

abstract = "The construction of a rational function that is nonnegative on two intervals of which one is infinite is considered. It is assumed that the maximum deviation of the function from zero on the infinite interval takes the minimum possible value under the condition that the values of the function on the finite interval are within the given bounds. It is assumed that the rational function (fraction) has the complete alternance. In this case, the original problem is reduced to solving a system of nonlinear equations. For solving this system, a two-stage method is proposed. At the first stage, a subsystem is selected and used to find a good approximation for the complete system. At the second stage, the complete system of nonlinear equations is solved. The solution is explained in detail for the case when the order of the fraction is between one and four. Numerical results for a fraction of order ten are presented.",

keywords = "rational functions, filtering problems, complete alternance, nonlinear systems of equations",

author = "V.N. Malozemov and G.Sh. Tamasyan",

year = "2017",

doi = "10.1134/S0965542517060100",

language = "English",

volume = "57",

pages = "919–930",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "6",

}

RIS

TY - JOUR

T1 - Synthesis of a Rational Filter in the Presence of Complete Alternance

AU - Malozemov, V.N.

AU - Tamasyan, G.Sh.

PY - 2017

Y1 - 2017

N2 - The construction of a rational function that is nonnegative on two intervals of which one is infinite is considered. It is assumed that the maximum deviation of the function from zero on the infinite interval takes the minimum possible value under the condition that the values of the function on the finite interval are within the given bounds. It is assumed that the rational function (fraction) has the complete alternance. In this case, the original problem is reduced to solving a system of nonlinear equations. For solving this system, a two-stage method is proposed. At the first stage, a subsystem is selected and used to find a good approximation for the complete system. At the second stage, the complete system of nonlinear equations is solved. The solution is explained in detail for the case when the order of the fraction is between one and four. Numerical results for a fraction of order ten are presented.

AB - The construction of a rational function that is nonnegative on two intervals of which one is infinite is considered. It is assumed that the maximum deviation of the function from zero on the infinite interval takes the minimum possible value under the condition that the values of the function on the finite interval are within the given bounds. It is assumed that the rational function (fraction) has the complete alternance. In this case, the original problem is reduced to solving a system of nonlinear equations. For solving this system, a two-stage method is proposed. At the first stage, a subsystem is selected and used to find a good approximation for the complete system. At the second stage, the complete system of nonlinear equations is solved. The solution is explained in detail for the case when the order of the fraction is between one and four. Numerical results for a fraction of order ten are presented.

KW - rational functions

KW - filtering problems

KW - complete alternance

KW - nonlinear systems of equations

U2 - 10.1134/S0965542517060100

DO - 10.1134/S0965542517060100

M3 - Article

VL - 57

SP - 919

EP - 930

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 6

ER -

ID: 7754161