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- W2516537412 abstract "A class of optimal polynomials is obtained satisfying constraints encountered in the design of electric band-pass filters having two levels of permissible attenuation in the pass band. Mathematically speaking, the x-axis is divided into six adjacent intervals, namely: (1) (- oo, 0) with no constraints; (2) (0, x ) and (x5, oc) with lower bound constraints; (3) (x_, x+) with upper bound constraints; and (4) (x_-, x_) and (x+, xi), called the transition regions, with no constraints, where O < x- < x - < 1 < x + < xs < oc. For a given degree, necessary and sufficient conditions are determined for the optimal polynomial which minimizes the width of the transition regions. These conditions turn out to be sufficient to characterize the optimal polynomial uniquely. An algorithm is also presented for deriving the optimal polynomial. The sequence of polynomials obtained in the iterations is proved to converge uniformly to the sought polynomial. 1. Introduction. The behavior of an electric band-pass filter is expressed by the filter transfer function H(iw), where o = 2 is called the radian frequency, f being simply the frequency." @default.
- W2516537412 created "2016-09-16" @default.
- W2516537412 creator A5086566225 @default.
- W2516537412 date "2016-01-01" @default.
- W2516537412 modified "2023-09-26" @default.
- W2516537412 title "A CLASS OF OPTIMAL POLYNOMIALS RELATED TO ELECTRIC" @default.
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