. The Bell System technical journal . ll functions may be assumed to be eithereven or odd with a period 2x. Thus, any amplitude approximating function 2 Ref. 4. DESIGN OF REACTIVE EQUALIZERS ni may he written in thec^^ (loniaiu as a Iourier cosine series, /l(v?) = <7o + (?! COS(^ + 02 cos 2^ + • + «« COS IKp = ^ fl^ COS k(p. (22) In particular, the correspondence of the x domain and <p domain may beconveniently illustrated as in Fig. 21. It is to be noted that the compara-tively limited region of the useful band, 0 < .v < 1, in the .v domain goes into half of the available range, 0
. The Bell System technical journal . ll functions may be assumed to be eithereven or odd with a period 2x. Thus, any amplitude approximating function 2 Ref. 4. DESIGN OF REACTIVE EQUALIZERS ni may he written in thec^^ (loniaiu as a Iourier cosine series, /l(v?) = <7o + (?! COS(^ + 02 cos 2^ + • + «« COS IKp = ^ fl^ COS k(p. (22) In particular, the correspondence of the x domain and <p domain may beconveniently illustrated as in Fig. 21. It is to be noted that the compara-tively limited region of the useful band, 0 < .v < 1, in the .v domain goes into half of the available range, 0 < (^ . Fig. 21—Graphical representation of the transformation x = tan ^. the Ak in eq. (14) to the au in eq. (22). This is accomplished by means of thefollowing relationships: X = tan /; — cos (f + cos (p 1 2 1 -~ X COS Hip = Vn (cos (p). Thus, the corresponding expression for eq. (22) in the frequency domainbecomes fi{<p) = ao + aiVi {cos<p) -f- 02^2 (cos^?) + azVz {cos(p) + -f dnVn {C0S() + ^1 COS if + ^2 COS- ip -\- bz CO?, ip -\- ■■■+ bn cos (p -^^• ^ (1 + xY + = /(.v^)/.(.v^), where /2(.v) = 1 (1 + .t2)» Therefore, it is necessary to predistort the approximatefl function B{x-) byredefining the /(</?) corresponding to /(.v-) as my where and n Mf) = IZ ^- cos A;(^ i=0 yt-X i=0 (1 + x^y = Mx), Hence,/i(/?), which corresponds to the approximating function/(.v-) multi- pUed by r- in the frequency domain, is the approximating function in \\ ~t~ X )the ip domain. In practice, the indicated predistortion of B{x-)
Size: 1826px × 1368px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
