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

The theory of narrow-band random processes is developed for probability density distributions of envelope and phase, and their derivatives in time of mixture of narrow-band Gaussian noise and a non-stationary slowly changing sinusoidal signal. Limiting forms of received distributions are obtained for the sum of a stationary sine wave and narrow band Gaussian noise. The special case of non-stationary signals is also discussed.