STATISTICAL ENERGY-FREQUENCY SPECTRUM 375 



signals and similar disturbances. The writer, however, concludes that 

 their application to "static" or "atmospheric" disturbances is of 

 questionable value owing partly to our lack of the necessary statistical 

 information regarding such disturbances and also to the fact that they 

 cannot be expected to have the "quasi-systematic" characteristics 

 necessary to the application of probability theory. 



The energy-frequency spectrum of a disturbance, as the concept is 

 here employed, will now be defined. Let a disturbance <E>(0 exist in 

 the epoch ^ t — T and let 



F(ico) = r(co) -f /.SXCO) 



= r $(/)e^"V/. (1) 



Then, as shown in my paper referred to above, 



1 /»«! rtT 



^Jo Jo 



The energy-frequency spectrum is defined by the equation 



G(co) = Lim4^|F(fco)|2, (2) 



so that 



r G{u:)d(^ = Lim^ r ^"-dt. (3) 



Jo T^^ ^ Jo 



It is on this last equation that the physical application of the concept 

 of the energy-frequency spectrum rests; namely, that it determines 

 the mean square value of $(/), as the epoch T is made indefinitely great. 

 Its principal application in electrotechnics depends upon the further 

 fact that, if $(/) represents an electromotive force applied to a net- 

 work of impedance Z{iw), the mean square current /- absorbed by the 

 network is given by ^ 



P = Lim i r Pdt = r .^^j^do^, (3a) 



T^^^X Jo kMI 



We now suppose that the function or disturbance $(/) is composed 

 of a number N of elementary disturbances ; thus 



Ht) = i:a,n<l>,nO - Un), (4) 



^A somewhat more involved formula gives the mean power absorbed. See my 

 paper referred to in the first paragraph. 



