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Article title OPTIMAL MATCHED FILTER FOR DETECTING THE SIGNAL AGAINST NOISE WITH THE UNKNOWN CORRELATION FUNCTIONS
Authors A.M. Makarov, A.S. Ermakov
Section SECTION I. METHODS AND ALGORITHMS FOR SIGNAL PROCESSIN
Month, Year 11, 2015 @en
Index UDC 621.37; 575.3; 519-21.519-27
DOI
Abstract To date, one of the unsolved problems of the theory of signal detection is the problem of synthesis of optimal signal detection in noise with completely unknown autocorrelation function. Especially true solution of this problem is the detection of complex wideband signals. In this article we propose an approach based on the synthesis of the matched filter in the signal space of the Mellin integral transform of the original additive mixture of signal and noise. As shown by the authors in a previous article this option appears on the basis of the fact that the correlation function of the random processes after integral Mellin transform is invariant to the form of the original autocorrelation function. The article presents the basic mathematical equations to prove the invariance property and is the main theorem, the results of which form the basis of this work. The proof shows that the value of the real part of the basic core functions of the Mellin transform based on the fundamental equality in signal processing theory – Parseval"s equality. Its value is equal to Ѕ. Next, using the classic mathematical apparatus of optimum synthesized in integral space of Mellin transform we matched filter algorithm and its structure. Block diagrams of the optimum matched filter is also provided. As an example, consider the spectral representation of harmonic vibrations in the basis of the integral Mellin transform. It is shown that the spectral density of the signal is permanent basis in the frequency spectrum Mellin. Changing the frequency of the harmonic signal source causes a change in amplitude of the response at the output of the Mellin transform. Received a spectral representation of a segment of harmonic oscillation having a finite duration. Thus, there is an opportunity for further study of the properties of the optimal filter for signals with a relative phase telegraphy. Phase shift keyed signals are widely used in most modern data transmission systems. These signals have the highest noise immunity among others manipulated signals. In general it can be concluded on the establishment of a new scientific direction in the theory of the development of a new generation of information transfer systems, possessing the property of invariance to the form of the correlation function of noise.

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Keywords Mellin transform; aprioristic indeterminacy of the correlation function of the noise; optimal matched filters; power spectrum density; Parseval equality; theorem of Wiener-Hinchey.
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