The method of discretization signals to minimize the fallibility of information recovery

Abstract

The paper proposes a fundamentally new approach to the formulation of the problem of optimizing the discretization interval (frequency). The well-known traditional methods of restoring an analog signal from its discrete implementations consist in sequentially solving two problems: restoring the output signal from a discrete signal at the output of a digital block and restoring the input signal of an analog block from its output signal. However, this approach leads to a methodical fallibility caused by interpolation when solving the first problem and by regularizing the equation when solving the second problem. The aim of the work is to develop a method for signal discretization to minimize the fallibility of information recovery to determine the optimal discretization frequency. The proposed method for determining the optimal discretization rate makes it possible to exclude both components of the methodological fallibility in recovering information about the input signal. This was achieved due to the fact that to solve the reconstruction problem, instead of the known equation, a relation is used that connects the input signal of the analog block with the output discrete signal of the digital block. The proposed relation is devoid of instabilities inherent in the well-known equation. Therefore, when solving it, neither interpolation nor regularization is required, which means that there are no components of the methodological fallibility caused by the indicated operations. In addition, the proposed ratio provides a joint consideration of the properties of the interference in the output signal of the digital block and the frequency properties of the transforming operator, which allows minimizing the fallibility in restoring the input signal of the analog block and determining the optimal discretization frequency. A widespread contradiction in the field of signal information recovery from its discrete values has been investigated. A decrease in the discretization frequency below the optimal one leads to an increase in the approximation fallibility and the loss of some information about the input signal of the analog-to-digital signal processing device. At the same time, unjustified overestimation of the discretization rate, complicating the technical implementation of the device, is not useful, since not only does it not increase the information about the input signal, but, if necessary, its restoration leads to its decrease due to the increase in the effect of noise in the output signal on the recovery accuracy. input signal. The proposed method for signal discretization based on the minimum information recovery fallibility to determine the optimal discretization rate allows us to solve this contradiction.