582 BELL SYSTEM TECHNICAL JOURNAL 



Here S/N is the ratio of root mean square audio signal and noise voltages. 

 The formula illustrates a general principle common to all the pulse systems 

 in that the marginal signal-to-noise ratio is a function of B/Nfr. The axes 

 of the curves have been labeled for .V = 1000 and/r = 8 kc, but can be read 

 for any other values of N and/r by changing B accordingly. Equation (7) 

 was used to plot the marginal power curve of Fig. 9. We note that the ratio 

 of rms pulse voltage at the top of the pulse to the rms noise voltage is 

 Ejy/l divided by £„/4 which leads to a value of eight when (5) is substituted. 

 The "sheer advantage" is thus the right-hand member of (7) divided by 

 eight. 



For CW interference in a PPM-AM system the procedure used above 

 applies except that the root mean square interference is now l/V^ times the 

 peak instead of one fourth. The marginal ratio of rms audio signal to rms 

 audio interference ratio is therefore poorer by a factor of 2v2> or 



^/^— ^K4-\ 



(8) 



When the interference is from a similar system, we calculate the distribu- 

 tion of the disturbance as follows. The probability that there is an inter- 

 fering pulse present during slicing is the ratio of the pulse duration to the 

 channel allotment, or 



p, = 2TNfr = '^-^\ (9) 



The interfering carrier will not, in general, be exactly synchronous with the 

 wanted carrier, and hence the actual interference is a beat frequency with 

 envelope having a voltage distribution calculable from the pulse shape. For 

 a sinusoidal pulse of height A, the probability p{y) dy that the instantaneous 

 magnitude of the interfering envelope is in the interval dy at }' is 



Since the relative phase of the two carriers drifts with time, the mean 

 square interfering voltage is half the mean square interfering envelope, or 



En = i ] y P(y) dy - -^^ = -^^. (11) 



Hence 



and 





