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Digital filtration in restoration problems continuous process on discrete samples


D. B. Rozhdestvenskii

At continuous process restoration on final number of discrete readout the technology of allocating function is used. Allocating function promotes ordering of a spectrum of the restored process regarding formation of a spectral line, concentrating energy in the main petal. For reception of allocating function filters of the bottom frequencies with suppression factor in a strip of a cut not less than 250 Дб are used. Existing technologies of synthesis of digital filters, do not allow to receive such characteristics. In the present work the method of construction of the digital filter possessing the necessary properties is stated. In a radio engineering the concept «the optimum filter» which characteristics find on the basis of knowledge of a spectrum of investigated process is known. In the article the processing case when the process spectrum is not known is considered. Rules of work with similar process are based on following reasons. Real processes are inherently characterised by integrated properties. For example, the temperature is the integrated characteristic of moving molecules. Many authors consider calculation of average values by exemplary operation, and the filter of sliding averaging as the reference filter. In the article the theory of the digital symmetric filters having the final pulse characteristic is offered. On the basis of the theory of symmetric filters the analysis of sliding averaging is carried out and its lacks are shown. As the reference filter it is offered to use the filter, the named filter of the corrected continuous averaging (CCA). Frequency characteristic CCA is equal to product of frequency characteristics of sliding continuous averaging and the ideal filter. To the greatest degree to the filter with such characteristic there corresponds the filter of the bottom frequencies constructed by approximation of the frequency characteristic by Chebyshev’s polynom. In the article the method of calculation of factors of the Chebyshev’s filter on the basis of digital symmetric filters is presented. The frequency characteristic of the Chebyshev,s filter has the least for the given number of factors of the filter width of the main petal, achievable at the set level of lateral petals.
June 24, 2020
May 29, 2020

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