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BELL SYSTEM TECHNICAL JOURNAL 



ual and it is difficult to assign a representative value. The crosses on figure 

 1 are obtained from his data when we assume that his filter behaves like a 

 low pass filter with a cutoff at fb = 2850, this choice being made in order 

 to make the maximum of his curve coincide with that of p{if). 



It is seen that some of the crosses lie above />(</?). This is probably due 

 to the fact that the actual filter differs somewhat from the assumed low pass 

 filter. 



On Fig. 1 there is also plotted a function closely related to (3.4-1). It 

 is the low pass filter form of the following: The probability of I passing 



Fig. 1 — Distribution of intervals between zeros — low-pass filter 

 j'xA(p is probability of a zero in Xtp when a zero is at origin. 



yn^v is probability of a zero in A(p when a zero is at origin and slopes at zeros are of 

 opposite signs. 



3'b — p{v)ifb = filter cutoff, r = time between zeros. 



through zero in t, t -\- dr when it is known that / passes through zero at 

 T = is 



where the notation is the same as in (3.4-1) and — - < tan H < - . 



This curve should always lie above p(<p) and the small difference between 

 the curves out to (^ = 4 indicates that [the true distribution of zeros is given 

 closely by p((p) out to this point. 



WTien (3.4-1) is applied to a relatively narrow band pass filter or some 

 similar device we may make some approximations and obtain an expression 

 somewhat simpler than (3.4-1). As a guide we consider our usual ideal 



