84 BELL SYSTEM TECHNICAL JOURNAL 



symmetrical about the mid-band frequency. We now go a step further and 

 assume an ideal band pass filter: 



W{f) = Wo fa <f <fb 



wif) = Otherwise (3.8-13) 



2fm = fa -\- fb 



Putting these in (3.8-2) we obtain zero for bi and 63 and also 

 bo = woifb — fa) = H 



(3.8-14) 



R = [2bo(a' - Df'z = [Uof'z 

 W " 13 J 



ifb -fa), « 2 = -— 



0^0 



n An n An 



1 4 6.775 



1 2.3 5 8.333 



2 3.735 6 9.9002 



3 5.238 7 11.4736 

 An r^ 1.5811 « + .3953 



From (3.8-12) we find that the expected number of maxima per second 

 of the envelope is 



N = MllOifb-fa) (3.8-15) 



assuming an ideal band pass filter. 



The distribution of the maxima of R for an ideal band pass filter may be 

 obtained by placing the results of (3.8-14) in (3.8-11). This gives 



_dR(f,--^ /-/.A3/2 



1^0 



,^,^UM^-.^-^^,(^J 



Z" An 



-rg+g 



