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CORRELATION FUNCTION OF THE LOGARITHMIC DERIVATIVE OF THE GAUSSIAN NOISE ENVELOPE

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A geometric representation of a random process is proposed. New vectors of the derivative of the envelope and the speed of rotation of the envelope vector are introduced in the graphical interpretation of the random process. Expressions for the envelope derivative and angular velocity have similar structures and are orthogonal projections of the same vector. The logarithmic derivative of the envelope and the derivative of the phase of a random process also have similar structures, close and even coinciding probabilistic characteristics. For a narrow-band Gaussian random process, a simple connection between their correlation functions is established.

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