382 BELL SYSTEM TECHNICAL JOURNAL 



Formulas (327) and (328) formulate the mean square current 

 and mean power absorbed by the branch of the network under con- 

 sideration, and enable us to calculate these quantities, even in the 

 case of complicated networks, with a minimum of labor. Formula 

 (327) is particularly well adapted to computation because the inte- 

 grand is everywhere positive, permitting, in most problems, of easy 

 numerical integration, whereas the anahtical solution may be com- 

 plicated. 



Formulas (327) and (328) have been applied to the theory of 

 selective circuits, to the problem of interference from random dis- 

 turbances, including static, and to the theory of the Schrotteffekt. 

 For the details of such applications, which will not be entered into 

 here, the reader is referred to the following papers. 



Transient Oscillations in Electric Wave Filters, Bell System 

 Technical Journal, July, 1923. 



Selective Circuits and Static Interference, Trans. A. I. E. E., 1924. 



An Application of the Periodogram to Wireless (Burch «& Bloeh- 

 msma), Phil. Mag., Feb., 1925. 



The Theory of the Schrotteffekt (Fry), Journal Franklin Institute, 

 Feb., 1925. 



The Building-Up of Alternating Currents 



Another application of the Fourier Integral, which may be briefly 

 mentioned, is to the building-up of alternating currents in response 

 to suddenly impressed sinusoidal electromotive forces. The investi- 

 gation of this problem is of great importance to the communication 

 engineer, since the excellence of a signal transmission system is to 

 a considerable extent determined by the duration and character of 

 the building-up phenomena. 



In long transmission systems the calculation of the building-up 

 current as a time function is extremely complicated and laborious 

 if not practically impossible. Furthermore we are usually not 

 concerned with the current as an instantaneous time function, but 

 rather with its envelope. The envelope of the current can be formu- 

 lated and calculated by mcxlified Fourier integrals, by the following 

 process. 



Suppose that an e.m.f. E cos wt is suddenly applied, at refer- 

 ence time t = 0, to a network of transfer impedance 



Ziicjo)=\Z{ic^)\ e'B^^K 



