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  5. Discrete symmetric ternary wavelet transform and its application in computerized systems of diagnostics and monitoring of parameters of processes and environments

Discrete symmetric ternary wavelet transform and its application in computerized systems of diagnostics and monitoring of parameters of processes and environments

A. Izmailov
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Description: The paper deals with the discrete wavelet transform based on symmetric ternary functions and its application effectiveness for reduction of memory volume required for data storage in computerized systems of diagnostics and monitoring of parameters of processes and environments. In the introduced transform two systems of wavelet functions are used instead of the usual one. The second system of wavelet functions was introduced in order to solve the problem of spectrum coverage due to the scaling parameter of the transform equal to three. The introduction of the second system of wavelet functions assured increased effec-tiveness of wavelet analysis of smooth functions. Besides, it was proved that the introduced discrete symmetric ternary wavelet transform is the orthogonal one. This property highlighted the high capabilities of the introduced transform for reducing the input data autocorrelation and leads to effective reduction of memory volume required for data storage without losing the high quality of data analysis. The filter form of the introduced transform was successfully implemented in the respective device. This device consists of both hardware and software components and was applied as the component of the complex for ground-based control and management of drilling oil and gas wells. Based on this implementation the effectiveness analysis was conducted in order to prove the application effectiveness of the introduced transform in systems of diagnostics and monitoring of parameters of processes and environments. The results showed not only greater reduction of memory volumes for data storage but also lower values of the recovery error in comparison to existing wavelet transforms. Due to the acquired results it is concluded that the discrete symmetric ternary wavelet transform combines simplicity of hardware and software implementation with high reduction of memory volume capabilities and effective detecting of high frequency characteristics of digital data imposed on the low fre-quency ones. The last property was inherited by the introduced discrete transform from the continuous one. Further studies consist of implementation of the discrete symmetric ternary wavelet transform in different devices designed for different special-ized systems of diagnostics and monitoring of parameters of processes and environments.


Keywords: digital information processing, symmetric ternary functions, discrete wavelet transform, wavelet functions, re-duction of memory volume.

References

Reference:
 Izmailov, A.V. (2019), “Dyskretne triikove symetrychne veivlet-peretvorennia ta yoho zastosuvannia u kompiuteryzovanykh systemakh diahnostuvannia ta kontroliu parametriv protsesiv i seredovyshch” [Discrete symmetric ternary wavelet transform and its application in computerized systems of diagnostics an monitoring of parameters of processes and environments], Information Processing Systems, Vol. 3(158), pp. 54-64. https://doi.org/10.30748/soi.2019.158.06.