Exploring the methods of spectral analysis of hydro-acoustic signals in space with l1-metric
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- Abstract
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We establish the main relationships characterizing both correlation and non-linear statistical interrelations between realizations of random samples in sample spaces with - and -metrics. On the basis of the obtained relationships for estimating the matrix of measure of statistical interrelation we develop instrumentation for utilizing known methods of spectral estimation (minimum variance method, eigenvector method, multiple signal classification method, minimum norm method) in signal spaces with -metric, thus, expanding their sphere of exploiting. New algorithms of hydro-acoustic signal spectral estimation have been developed. These algorithms are built on the basis of general approach based on generalized metric spaces with L-group properties. The main feature of this approach allows decreasing computational requirements to signal processing system, inasmuch as the main part of signal processing operations is fulfilled without multiplication operation, i.e. the developed algorithms of spectral analysis are «almost» multiplication-free. We accomplish the comparative analysis between the developed and known algorithms of spectral estimation. It is shown that the developed algorithms based on signal space with -metric and L-group properties provide the same resolution in frequency as the linear algorithms based on signal space with - metric do.
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- 2024-12-31
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Copyright (c) 2024 Олексій Налапко,Сергій Зібін,Андрій Попов,Володимир Твердохлібов
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