Abstract
In this paper a modified wavelet synthesis algorithm for continuous wavelet transform is proposed, allowing one to obtain a guaranteed approximation of the maternal wavelet to the sample of the analyzed signal (overlap match) and, at the same time, a formalized representation of the wavelet. What distinguishes this method from similar ones? During the procedure of wavelets’ synthesis for continuous wavelet transform it is proposed to use splines and artificial neural networks. The paper also suggests a comparative analysis of polynomial, neural network, and wavelet spline models. It also deals with feasibility of using these models in the synthesis of wavelets during such studies like fine structure of signals, as well as in analysis of large parts of signals whose shape is variable. A number of studies have shown that during the wavelets’ synthesis, the use of artificial neural networks (based on radial basis functions) and cubic splines enables the possibility of obtaining guaranteed accuracy in approaching the maternal wavelet to the signal’s sample (with no approximation error). It also allows for its formalized representation, which is especially important during software implementation of the algorithm for calculating the continuous conversions at digital signal processors and microcontrollers. This paper demonstrates the possibility of using synthesized wavelet, obtained based on polynomial, neural network, and spline models, during the performance of an inverse continuous wavelet transform.
Highlights
Modern signal processing systems face more and more sophisticated requirements, dealing with accuracy of information signs in the signal
The contribution of this article can be summarized as follows: 1. We have proposed a modified algorithm for the synthesis of wavelets for continuous wavelet transform, which differs from the known ones by the guaranteed accuracy of approximation of the parent wavelet to a given sample, with the possibility of a formalized representation of the wavelet
This algorithm allows one Sensors 2021, 21, 6416 to solve an important practical problem. It allows synthesizing wavelets, which can later be used to perform continuous wavelet transform on an element base, where it is important to have a formalized representation of the basic function
Summary
Modern signal processing systems face more and more sophisticated requirements, dealing with accuracy of information signs (features) in the signal. We have proposed a modified algorithm for the synthesis of wavelets for continuous wavelet transform, which differs from the known ones by the guaranteed accuracy of approximation of the parent wavelet to a given sample (overlap match), with the possibility of a formalized representation of the wavelet This algorithm allows one Sensors 2021, 21, 6416 to solve an important practical problem. It allows synthesizing wavelets, which can later be used to perform continuous wavelet transform on an element base, where it is important to have a formalized representation of the basic function (microcontrollers, digital signal processors, graphics processors, etc.).
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