Origin and properties of own error signals of the discrete wavelet transform algorithms

• Autorzy: Dróżdż Łukasz , Roj Jerzy

Identyfikatory

DOI

10.24425/ijet.2024.149591

• Języki publikacji: EN

Abstrakty

EN

The article presents a method for analyzing the own errors of the discrete wavelet transform algorithms, which are introduced by these algorithms into the output quantities. The presented considerations include determining the origin of the error signals in question and determining their parameters. Both errors resulting from imperfections in the transmittance of the algorithm and those resulting from its implementation in the actual measurement chain were considered.

Słowa kluczowe

EN

wavelet transform; uncertainty budget; uncertainty estimation; wavelet transform own errors

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2024
• Tom: Vol. 70, No. 3
• Strony: 643--648
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Dróżdż Łukasz

• Silesian University of Technology

autor

Roj Jerzy

• Silesian University of Technology

Bibliografia

• [1] K. A. Ahmad, Wavelet Packets and Their Statistical Applications. Springer Singapore, 2018.
• [2] P. S. Addison, The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance, 2nd ed. CRC Press, 2017.
• [3] C. M. Akujuobi, Wavelets and Wavelet Transform Systems and Their Applications. Springer, 2022.
• [4] A. Z. Averbuch, P. Neittaanmäki, and V. A. Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, 2019, vol. 3.
• [5] A. Singh, A. Rawat, and N. Raghuthaman, Mexican Hat Wavelet Transform and Its Applications. Springer, 2022, pp. 299-317.
• [6] L. Dróźdź, M. Kampik, and J. Roj, “Estimation of the resultant expanded uncertainty of the output quantities of the measurement chain using the discrete wavelet transform algorithm,” Applied Sciences, vol. 14, no. 9, 2024. [Online]. Available: http://doi.org/10.3390/app14093691
• [7] L. Dróźdź and J. Roj, “Propagation of random errors by the discrete wavelet transform algorithm,” Electronics, vol. 10, no. 7, 2021. [Online]. Available: http://doi.org/10.3390/electronics10070764
• [8] L. Dróźdź, M. Kampik, and J. Roj, “Error model of a measurement chain containing the discrete wavelet transform algorithm,” Applied Sciences, vol. 14, no. 8, 2024. [Online]. Available: http://doi.org/10.3390/app14083461
• [9] S. Mallat, A wavelet tour of signal processing, 3rd ed. Academic Press, 2008.
• [10] D. S. Reay, Digital Signal Processing Using the ARM Cortex M4. John Wiley & Sons, 2015.
• [11] CMSIS-DSP - Embedded compute library for Cortex-M and Cortex-A, ARM Limited, 2023.
• [12] Z. Průša, P. L. Søndergaard, and P. Rajmic, “Discrete wavelet transforms in the large time-frequency analysis toolbox for matlab/gnu octave,” ACM Transactions on Mathematical Software (TOMS), vol. 42, no. 4, pp. 1-23, 2016. [Online]. Available: http://doi.org/10.1145/2839298
• [13] M. Misiti, Y. Misiti, G. Oppenheim, and J. M. Poggi, Wavelet toolbox, The MathWorks Inc., 2018.
• [14] G. Lee, R. Gommers, F. Waselewski, K. Wohlfahrt, and A. O’Leary, “Pywavelets: A python package for wavelet analysis,” Journal of Open Source Software, vol. 4, no. 36, p. 1237, 2019. [Online]. Available: http://doi.org/10.21105/joss.01237
• [15] F. Benz, F. Hildebrandt, and S. Hack, “A dynamic program analysis to find floating-point accuracy problems,” ACM SIGPLAN Notices, vol. 47, no. 6, pp. 453-462, 2012. [Online]. Available: http://doi.org/10.1145/2345156.2254118
• [16] C. Vonesch, T. Blu, and M. Unser, “Generalized daubechies wavelet families,” IEEE Transactions on Signal Processing, vol. 55, no. 9, pp. 4415-4429, 2007. [Online]. Available: http://doi.org/10.1109/TSP.2007.896255
• [17] A. V. Oppenheim and R. W. Schafer, Discrete-time signal processing, 3rd ed. Pearson, 2009.
• [18] A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems, 2nd ed. Pearson, 2013.
• [19] J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Princi-ples, Algorithms and Applications, 5th ed. Pearson, 2021.
• [20] Joint Committee for Guides in Metrology, Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement, JCGM, 2008. [Online]. Available: https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf
• [21] H. Janssen, “Monte-carlo based uncertainty analysis: Sampling efficiency and sampling convergence,” Reliability Engineering & System Safety, vol. 109, pp. 123-132, 2013. [Online]. Available: http://doi.org/10.1016/j.ress.2012.08.003
• [22] Joint Committee for Guides in Metrology, Evaluation of measurement data - Propagation of distributions using a Monte Carlo method, JCGM, 2008. [Online]. Available: https://www.bipm.org/documents/20126/2071204/JCGM_101_2008_E.pdf
• [23] M. K. Urbanski and J. W ˛asowski, “Fuzzy approach to the theory of measurement inexactness,” Measurement, vol. 34, no. 1, pp. 67-74, 2003. [Online]. Available: http://doi.org/10.1016/S0263-2241(03)00021-6
• [24] R. M. Stallman et al., Using the GNU Compiler Collection, Free Software Foundation, 2023.
• [25] D. Wei, Coiflet-type wavelets: theory, design, and applications, The University of Texas at Austin, 1998.
• [26] Cortex-M4 - Technical Reference Manual, ARM Limited, 2010.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).