Probability distributions of the envelope and phase, and their derivatives in time of the sum of a non-stationary sine signal and narrow-band Gaussian noise (Q5926839)

Based on former results on the superposition of narrow-band Gaussian noise and sinusoidal signals, the paper is considering the problem of the superposition of Gaussian noise with a non-stationary sinusoidal signal with spectral width less than that of the noise. The probability distribution of the envelope, of its derivative in time, of the phase, and of its derivative in time are calculated and compared with the results of the stationary case. Furthermore, a special case is discussed that arises in certain crystal oscillators.