Probabilistic Characteristics of the Envelope Derivative for the Sum of Signal and Narrow-Band Noise

摘要

Probability density and the formula for moments of the envelope derivative of the sum of harmonic signal and Gaussian narrow-band noise have been obtained. A new random function equal to the product of the envelope and phase derivative was introduced and the same probabilistic characteristics were determined for this function. Geometrical interpretation of the sum of signal and noise implies that the introduced function represents angular speed of rotation of the resultant vector.