On the Geometric Pattern Transformation (GPT) Properties of Unidimensional Signals

  • Cristian Bonini Research, Development, and Innovation in Electrical Energy Center, Universidad Tecnológica Nacional Facultad Regional General Pacheco, Av. Hipólito Yrigoyen 288, B1617, General Pacheco, Argentina https://orcid.org/0000-0001-8421-1339
  • Marcos Maillot Research, Development, and Innovation in Electrical Energy Center, Universidad Tecnológica Nacional Facultad Regional General Pacheco, Av. Hipólito Yrigoyen 288, B1617, General Pacheco, Argentina https://orcid.org/0000-0002-4071-5540
  • Dino Otero Vehicle Research, Development, and Innovation Center, Universidad Tecnológica Nacional Facultad Regional General Pacheco, Av. Hipólito Yrigoyen 288, B1617, General Pacheco, Argentina
  • Andrea Rey Center of Research and Development in Applied Informatics, Universidad Nacional de Hurlingham, Tte. Manuel Origone 151, B1688, Villa Santos Tesei, Argentina https://orcid.org/0000-0002-9185-1382
  • Ariel Amadio Vehicle Research, Development, and Innovation Center, Universidad Tecnológica Nacional Facultad Regional General Pacheco, Argentina
  • Walter Legnani Signal and Image Processing Center, Universidad Tecnológica Nacional Facultad Regional Buenos Aires, Argentina
DOI: https://doi.org/10.19139/soic-2310-5070-1924
Keywords: Phase Space, Tied Data, Noise Characterization, Forbidden Patterns, Fixed Point

Abstract

The Geometric Pattern Transformation (GPT) has several advantages of use concerning contemporary algorithms that have been duly studied in previous research. Regarding some of its properties, four different but complementary aspects of the GPT are presented in this work. After a brief review of the GPT concept, how tied data are manifested in data sets is shown, to obtain a symmetric representation of the GPT, a linear transformation is performed that regularizes the geometric representation of the GPT and the theoretical relationship between the GPT and the phase-state representation of 1D signals is analyzed and formalized, then the study of the forbidden pattern is easily revealed, obtaining a strong relationship with the stable and unstable fixed points of the logistic equation. Finally, the characterization of colored noises and the application in real world signals taken through experimental procedures is analyzed. With these results, in this work is proposed an advance in the potential applications of the GPT in an integral way in the processing and analysis of data series.
Published
2024-08-25
How to Cite
Bonini, C., Maillot, M., Otero, D., Rey, A., Amadio, A., & Legnani, W. (2024). On the Geometric Pattern Transformation (GPT) Properties of Unidimensional Signals. Statistics, Optimization & Information Computing, 12(6), 2000-2021. https://doi.org/10.19139/soic-2310-5070-1924
Issue
Vol 12 No 6 (2024)
Section
Research Articles
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