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BELL SYSTEM TECHNICAL JOURNAL 



proximating functions are available which make it a relatively simple 

 matter to design physically realizable networks exhibiting this property of 

 a sharp cut-oflf to zero outside the useful band.^^ However, a similar method 

 of applying Tchebycheff polynomials to transfer characteristics which vary 

 with frequency in a prescribed manner over a finite band has not been 

 evolved. In order to illustrate the preceding statements, Figs. 12 and 13 

 have been included as representative of typical transfer characteristics. 



Fig. 12 — Transfer characteristic for impedance matching or low-pass filter case. 



Fig. 13 — Transfer characteristic for reactive equalizer case. 



3. Derivation or Special Transfer Function 



In accordance with the brief discussion at the conclusion of the previous 

 chapter, it is now appropriate to state that it is the purpose of this paper (1) 

 to derive a transfer function which is especially suited to the problem of 

 reactive equalization, and (2) to develop a systematic method which utilizes 

 this special transfer function to approximate satisfactorily, with a finite 

 number of network elements, a specified transfer characteristic over the 

 entire frequency spectrum. This section will consider in detail the first of 

 these two main tasks in the formulation of a design method for reactive 

 equalizers. 



With reference to Fig. 13, it is convenient to divide the complete transfer 



" Ref. 4. Also Ref. 2, pp. 53-79. 



