DOI 10.17586/0021-3454-2023-66-9-798-802
UDC 621.376
CORRELATION FUNCTION OF THE LOGARITHMIC DERIVATIVE OF THE GAUSSIAN NOISE ENVELOPE
Bauman Moscow State Technical University, Department of Radio Electronic Systems and Devices;
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Reference for citation: An V. I. Correlation function of the logarithmic derivative of the Gaussian noise envelope. Journal of Instrument Engineering. 2023. Vol. 66, N 9. P. 798—802 (in Russian). DOI: 10.17586/0021-3454-2023-66-9-798-802.
Abstract. 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.
Abstract. 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.
Keywords: geometric representation of random process, Gaussian random process, derivative of phase, logarithmic derivative of envelope, random frequency, correlation function
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