610 BELL SYSTEM TECHNICAL JOURNAL 



where 



I\, I2, ' ' ' Tn = average intensities of the sources 1,2, • ■ • n, 

 mi, W2, • • • Wn = number of peaks of each source per minute, 



n 



N = X^ m,- = total number of source peaks per minute. 



If several source peaks occur in the same 0.2 second interval, they 

 will appear as a single composite peak on the meter. On the assump- 

 tion of discrete 0.2 second intervals, these source peaks coincide. 

 Their intensities, consequently, add up directly. For instance, if two 

 source peaks occur during each integration period, the average inten- 

 sity of the composite noise will be twice the arithmetic mean of the 

 intensities. Similarly, the average intensity of the composite noise, 

 when the number of source peaks per 0.2 second interval averages a, 

 will be 



Let M = the total number of composite noise peaks per minute. 

 The maximum value that M can have is 300, the number of integra- 

 tion periods per minute. Unless the composite noise is continuous, 

 however, there will be a certain proportion of time, to, in which no 

 composite peaks occur. M then can be determined from the relation : 



M = (1 - to) 300. (4) 



If, on the average, a source peaks per 0.2 second occur, the following 



relation holds between the total number of source peaks, N, and the 



number of composite peaks: 



TV 

 ilf = - . (4a) 



a 



Introducing this expression in equation (3) gives 



As shown by equation (4), M is a function of to, the proportion of time 

 in which no composite noise peaks occur. The value for to can be 

 found, as follows: The proportion of time when source j has a peak is 

 equal to the probability pj = m,/300, and the proportion of time when 

 source j has no peak is 5,- = 1 — />,• = 1 — (m,/300) . The proportion 

 of time, to, when there are no peaks from anysource then is equal to 



