Vol. 16, no.1, 2024
РусскийEnglish
RADIOELECTRONICS
Physically realizable reconstruction of a continuous signal after sampling
Andrey N. Degtyarev, Igor L. Afonin, Alexander L Polyakov
Sevastopol State University, http://www.sevsu.ru/
Sevastopol 299053, Russian Federation
E-mail: andegtyarev@mail.sevsu.ru, ilafonin@mail.sevsu.ru, alpolyakov@ mail.sevsu.ru
Received August 23, 2023, peer-reviewed August 30, 2023, accepted September 07, 2023, published March 15, 2024.
Abstract: It is proposed to describe signals in a physically realizable basis. Correlation functions of impulse characteristics of physically implemented filters are used as basic functions. To obtain analytical expressions of the functions of the proposed physically realizable basis, it is proposed to use inverse Fourier transforms from approximations (Butterworth, Chebyshev, etc.) of the squares of the amplitude-frequency characteristics of normalized low-pass filters. The basis, functions are copies of the indicated correlation functions of the impulse characteristics, shifted relative to each other by the same time interval, which is the sampling interval. It is shown that there is a sampling theorem in the space of the introduced functions. The exact restoration of the signal is possible if the functions of the considered basis have the property of readability. In this case, the considered basic functions are functions of counts and are not physically implemented. To reduce the error of restoring a continuous signal from its readings using the proposed basis, it is necessary to increase the order of the filter, the pulse characteristics of which are used in the formation of the basis. To restore a continuous signal, its samples must be fed to two cascaded filters. The first filter must have an impulse response, the correlation function of which is used to form a physically realizable basis. The second filter must be matched to the impulse response of the first filter.
Keywords: sampling, sampling theorem, pulse characteristic of the filter, correlation function
UDC 621.376.5
RENSIT, 2024, 16(1):3-10e DOI: 10.17725/j.rensit.2024.16.003
Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/536/16(1)3-10e.pdf