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A way to improve the quality of graphical data digitising

This paper considers the actual problem of graphical information converting back into raw data format that was used to represent it. This is due to the great scientifi achievements contained in editions from the Soviet period, as well as the intention global publishers from "unfriendly" countries to close access for Russian and Belarusian organisations to scientific publications and technical information databases. As a result, Russian scientists can only have graphical materials in formats similar to PDF documents. This paper considers a fairly simple way of solving this problem when digitising graphs in printed or electronic publications with low resolution and a large picture scale, which does not allow to detail its separate fragments. The procedure for pre-processing the original image in bitmap format is described. In order to improve the numerical data resulting accuracy from the subsequent digitising, a number of features are recommended, which are available in the well-known and most common graphical editors. These functions include changing the color mode of the image, color inversion, sharpening and contrast, linear scaling (vertical and horizontal scaling), and graph line spline approximation. The above operations are accessible to users with the minimum familiarity of graphical editors Microsoft Power Point and Adobe Photoshop. As an developed procedure use example, the results of FRB 160317 signal digitising (a so-called Fast Radio Burst), are presented. The digitising of its graphical image has provided more accurate additional information on signal characteristics not given by publication authors. A visual evaluation of the digitised FRB 160317 signal accuracy by matching it with the original graphical image is presented, which showed a satisfactory match to the original. The numerical data array obtained by digitising the raw graphical material using a pre-processing procedure is becomes available for further analysis. The described way can be used by university teachers both at the initial stages of students teaching to work with images and carry out data analysis, and when preparing teaching materials when organising the educational process using distance learning technologies. The results are applicable at the starting stages of scientifi research in the initial data set formation for dependency analysis in various subject areas, where there are no initial samples refl the results of observation. Read more...

Piecewise linear approximation of a highly noisy signal waveform using least squares method

The rising trend of computer technology using makes digital signal processing (DSP) techniques converted into numerical data sets particularly relevant. For the most part, they are quite complex and their use is not always justified for a wide range of applications. This determines the ongoing interest in heuristic algorithms that are based on simplified approaches and allow quickly obtaining approximation of estimates with the least work amount. This paper discusses a method of pulsed (single) aperiodic signal with a high level of noise component mathematical processing by approximating its shape by a piecewise linear function, that parameters are determined using the method of least squares. A brief justification for this method is given, based on an analysis of the stochastic nature of the noise component. A numerical analysis of the signals spectral composition before and after processing is performed, as well as a comparison with other common methods: filtering and coherent averaging. It is shown that the waveform piecewise linear approximation can effectively separate the useful signal from the noise component, does not require complex algorithmic designs, and its program code implementation is possible in any high-level languages. The developed method is applicable for all types of signals and is most effective for processing single aperiodic pulses without its repetition possibility. The proposed approach can also be used in the educational process when studying the programming basics and for solving economic problems based on the determination of trend lines by parametric methods. Read more...

Accuracy estimating of highly noisy signals digital processing using heuristic algorithms

Heuristic algorithms are often used as an alternative when solving problems of high computational complexity or lacking an exact solution, allowing to quickly obtain the desired result. Usually, they do not have a strict mathematical justification, but their application is justified in terms of practicality. Formally, algorithms that use approximate methods can be classified as heuristic. However, when applying them, the problem of determinism lack is often arises, which does not always allow one to evaluate the solution obtained accuracy. The paper considers a methodical approach to assessing the accuracy of heuristic algorithms designed to determine the useful signal shape and parameters on the strong noise component background. It is based on the method of analogy and consists in modeling an artificial signal with given parameters and a background noise interference similar in its characteristics to additive white Gaussian noise. In this case, the noise component is formed by software using a pseudo-random number sequence generator. Such generators are included in the packages of almost all high-level programming languages built-in functions. A comparative analysis of the real and artificial noise characteristics is presented, that shown the problem solving by numerical modeling possibility. The results of accuracy estimation in determining the artificial signal parameters, that is separated from the noise component using piecewise linear approximation and averaging heuristic algorithms, are obtained. The problem of empirical data smoothing with the discrete signal equivalent replacement by a quadratic functions whose parameters provide a piecewise parabolic approximation its shape is also considered. This procedure eliminates the residual signal bounce that inevitably occurs as a result of linearization and allows further recording at any sampling rate. Thus, the proposed approach allows us to quantify the accuracy of heuristic algorithms used in determining the expected signal parameters. Read more...