586 BELL SYSTEM TECHNICAL JOURNAL 



cos \2tt{c + n\) (^ + ^^ 7) " ^ ' ^ = 0' =1=1' ±2, • • • (36) 



Averaging the square over all values of Imir — — + ctt , which may be 



treated as a randomly distributed angle, we find an expression for hi averaged 

 over the values at the slicing instants and not over all time, viz.: 



5l = ^^ Fl{R' + X') (37) 



where R ^ X (c + n\)An cos mr\ ( 1 + — 7— M 



(38) 



Then 



and 



X= f. {c + n\)An sin LttX (l + ^^1 (39) 



r. = »tZl) («) 



For each value of 5, the value of S/I should be computed over a range of 

 values of c; and the lowest value of S/I, corresponding to the most unfavor- 

 able allocation of the CW frequency, plotted as a point on the curve. The 

 curve of Fig. 12 was not calculated in this way but estimated from the sim- 

 pler solution existing when the pulses are contiguous. 



When the interference is from a similar system, we substitute for the inter- 

 fering wave : 



F2(0 = Q cos [lirfil + 4>{t - r) + d] (42) 



This gives 



5(^) = ^ i sin [0(/) -4>{t-r) -d^ 2,r(/i - fM (43) 



27rjr at 



We distinguish between the cases of overlapping and non-overlapping pulses. 



