Axis-Crossings of the Phase of Sine Wave Plus Noise
01 April 1967
Consider the stationary random process I(t,a) consisting of a sinusoidal signal of amplitude V 2 a and frequency f0 plus Gaussian noise /*( of unit variance, having a narrow-band power spectral density Wb(f -- f0) which is symmetric about j0 . Rice's 1 graphical representation of I(t,a) is illustrated in Fig. 1 in order to define the Rayleigh envelope process R(t,a) and the resultant phase -- TT ^ 9(t,a) ^ TT. The purpose of this 737 738 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1967 Fig. 1 -- Graphical representation of I(t,a) = V2 a cos 2ir/01 + /jv(0 = R(t,a) cos [27t/0