112 



"BELL SYSTEM TECHNICAL JOURNAL 



are shown in Figs. 1 and 2. The curves for a = 10 and a = \/l0 were com- 

 puted by Simpson's rule from (1.6) and (1.7), and the curves ior a = 1 

 were computed from the series (1.10) given below. Since both (p(x) and 



Hn 



%|~ 



1.5 



1.0 

 0.75 



0.5 

 0.4 



0.3 



0.2 

 0.15 



0.1 



0.075 



> 0.05 

 0.04 



0.03 



0.02 

 0.015 



0.01 

 0XX)75 



0.005 



0.2 OA 



2.6 



0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 



1/ (RMSI) 



Fig. 1 — Probability density of sine wave plus noise. 

 / - Qcm qtj- In, a - Q/V^, y = I/V^, V^ = rms ly 

 Piiy) dl/y/rf'o - probability total current lies between / and I -\- dl 

 y(l + flV2)~*/' " //(rms /). Curves are symmetrical about y = 0. 



<p-i(x) are tabulated^ functions the integrals in (1.6) and (1.7) are well 

 suited to numerical evaluation. 



« \^W.'* li^^" directly and ip-iix) may be readily obtained from W.P.A., "Tables of 

 Probability Functions," Vol. II, New York (1942). The functions <p^"'\y) are tabulated 

 SoS "Probability and its Engineering Uses" by T. C. Fry (D. Van Nostrand Co., 



1928). 



