592 BELL SYSTEM TECHNICAL JOURNAL 



When instantaneous sampling is used instead of a gate, the value of c„ 

 becomes a constant for all values of n of interest and is equal to a^. We then 

 find: 



on r :^2(l-c) / ^A2 "1-1/2 



Here c is to be selected to make S/I minimum for each value of x. The 

 poorest values of S/I occur when Bessel functiojis of comparable order and 

 argument appear in the summation, which means that c is in the neighbor- 

 hood of —x/2. The corresponding difference between the CW and mid- 

 carrier frequencies is one-fourth the peak-to-peak swing. 

 To calculate the interference between two similar idle systems, we set 



(78) 



(79) 



V{t) = Pcos ilTrfit -f- Jr sin TrFbtj 



-f Q cos \2irf2t + Jr sin {-kF^I - d)\ 



The frequency error registered in the first system is then 



hit) = -^ ^ sin [27r(/i - U)t -1- X sin irFbl - x sin {irFbt - e)] 

 2-wP at 



= -^ - sin 2r{fi - f2)t + 2x sin - cos iirFbl - -j 



• cos 27r I /i - /2 + -y- ) t - yJ • 

 It follows that the response of the baseband filter is 

 m = ^^ E^ {c + I) /. (2. sin cos [2.F. {c + 1) t - .n ^ . 



(80) 



The effects of the channel gate and filter are computed in the same way as 

 for CW, giving the audio interference: 



cos ( 27r[(2c -f m)^ -\- n]frt - m -j 



(81) 



