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

Eduardo Trutié-Carrero, Diego Seuret-Jiménez and José M. Nieto-Jalil
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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

Mathematics, 2021, vol. 9, issue 23, 1-17

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.

Keywords: frequency spectrum; multi-sensitivity; Te-periodogram; Te-transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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