. The Bell System technical journal . f the transfer characteristic while the other produces the de-sired cut-off characteristic. The derivation of the desired denominator, B{x-), begins by writing thetransfer characteristic of Fig. 14 for the in-band region as 1 B{x Ke 2k/M 15 (10) In order to make the following derivation clear, it is suggested that the discussionof Tchebycheff polynomials, pp. 733-734, be examined at this time. *The transmission a = ao + kf(x) will be written as kf(x) for the remainder of thisanalysis. The general transmission level ao may be found in the final stages of a
. The Bell System technical journal . f the transfer characteristic while the other produces the de-sired cut-off characteristic. The derivation of the desired denominator, B{x-), begins by writing thetransfer characteristic of Fig. 14 for the in-band region as 1 B{x Ke 2k/M 15 (10) In order to make the following derivation clear, it is suggested that the discussionof Tchebycheff polynomials, pp. 733-734, be examined at this time. *The transmission a = ao + kf(x) will be written as kf(x) for the remainder of thisanalysis. The general transmission level ao may be found in the final stages of a particulardesign when the impedance level is adjusted to conform with the prescribed C„. 730 BELL SYSTEM TECHNICAL JOURNAL 111 terms of B{x~) directly and a desired transmission ao at the angular cut-off frequency coo, equation (10) becomes ^(.^2) = /ao^- -2fc/(i) (11) where A = ^~^°. Equation (11) now represents the characteristic that isto be approximated over the useful frequency band while Fig. 15 shows aplot of this Fig. 15—Specification for B{x) over useful frequencj* band. /f(x2)+f2V^2(x) f2Vn2(x)
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