G48 THE BELL SYSTEM TECHXICAL JOURNAL, MAY 1957 



where 



Rs(t) = f Wsif) cos 2TfTdf (5) 



and Wsif) is the power spectrum of the applied signal S(t). The last ex- 

 pression in (4) follows from the next to the last by analogy ^^'ith equation 

 (1.14) of Reference 1. 



The dc component of the distortion d'(t) is its average value d' which 

 may be computed from 



e'' = Re>(o.) = ^' r^V^l - cos2pr)] (6) 



This follows from (4) since Rs (^) = 0. 



The auto-correlation function of the distortion, excluding the dc 

 component, is then 



R,,_r. = ^ [e~''Rs'''][(e'''Rs'''- I) - {e'''^^'^' - 1) cos 2pr] (7) 



The mterchannel interference spectrum is 



Wc{j) = 4 /" Rcir) cos 27rfr dr (8) 



where, by analogy with equation (1.22) of Reference 1, 



E^{r) = ^' [e-''Rs'''][(e''-'^''> - T'Rs{t) - 1) 



^ (9) 



_ ^^-r'^sir) ^ j.2^^(^) -1 ) cos 2pT] 



As mentioned before, the function wdf) is of interest because 



P, = Waif) df (10) 



is the average interference power appearing at the receiver in an idle 

 channel of width df centered on frequency' /. 



RATIO OF IXTERCHAXXEL IXTERFEREX'CE TO SIGXAL POWER 



The average signal power appearing in a bus\' channel of width df 

 centered on the frequency / is 



Ps = Wsif) df (11) 



and hence the ratio of the interchannel interference power to the signal 



