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A High-Resolution Dyadic Transform for Non-Stationary Signal Analysis

Author

Listed:
  • Eduardo Trutié-Carrero

    (Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Chamilpa 62209, Morelos, Mexico)

  • Diego Seuret-Jiménez

    (Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Chamilpa 62209, Morelos, Mexico)

  • José M. Nieto-Jalil

    (Tecnologico de Monterrey, School of Engineering and Sciences, Blvd. Enrique Mazón López 965, Hermosillo 83000, Sonora, Mexico)

Abstract

This article shows a new Te-transform and its periodogram for applications that mainly exhibit stochastic behavior with a signal-to-noise ratio lower than −30 dB. The Te-transform is a dyadic transform that combines the properties of the dyadic Wavelet transform and the Fourier transform. This paper also provides another contribution, a corollary on the energy relationship between the untransformed signal and the transformed one using the Te-transform. This transform is compared with other methods used for the analysis in the frequency domain, reported in literature. To perform the validation, the authors created two synthetic scenarios: a noise-free signal scenario and another signal scenario with a signal-to-noise ratio equal to −69 dB. The results show that the Te-transform improves the sensitivity in the frequency spectrum with respect to previously reported methods.

Suggested Citation

  • Eduardo Trutié-Carrero & Diego Seuret-Jiménez & José M. Nieto-Jalil, 2021. "A High-Resolution Dyadic Transform for Non-Stationary Signal Analysis," Mathematics, MDPI, vol. 9(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3041-:d:689090
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