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Article title INTERRELATION OF AUTOCORRELATED FUNCTION OF STATIONARY CASUAL PROCESSES IN BASIS OF THE FURYE TRANSFORMATION FROM THE SPECTRAL DENSITY OF POWER IN BASIS OF THE MELLIN TRANSFORMATION (ANALOG OF VINER-HINCHIN THEOREM)
Authors A.M. Makarov
Section SECTION I. METHODS AND ALGORITHMS FOR SIGNAL PROCESSING
Month, Year 11, 2014 @en
Index UDC 519.21
DOI
Abstract The mathematical apparatus of the Fourier integral led to the creation of the theory and methods of synthesis of optimal algorithms for signal detection, estimation of their parameters from the background noise. The appearance in the last 20–30 years of complex signals with frequency hopping, a pseudo-random frequency hopping, δ-modulated wideband frequency- modulated signals has led to the need to consider the form of the correlation function of noise. The main task of the modern theory of signal detection on the background noise is to reduce the degree of freedom of the thresholds of decision rules to the unknown "interfering" signal and noise parameters. Especially formidable task is to create new methods for efficient detection of signals from the background noise with unknown correlation function. In the article the mathematical formalism of the Mellin integral transformation processes with random; in this basis is established the relationship of power spectral density of random processes and the correlation function, the analogue of the Wiener–Khinchin. Thus, up to a constant factor, noise power spectral density of the invariant to the form after its initial correlation function. On this basis it is possible to develop a mathematical formalism of the synthesis of optimal algorithms for detecting signals from the background noise with their unknown correlation function.

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Keywords Melinn's transformation; autocorrelation; the spectral power density of the random process; unknown correlation function; detection of signals.
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