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.
Highlights
Mathematics 2021, 9, 3041. https://This paper presents three contributions
The second addresses the dyadic Te-periodogram (DTeP), and the last contribution shows a corollary on the energy conservation of the transformed signal by Te-transform
To carry out this work, the authors relied on the properties of the Fourier transform (FT), the dyadic Wavelet transform (DWT), and the Welch–Bartlett periodogram (WBP)
Summary
The authors in [14] show a procedure in which their main objective is to represent a spectrogram based on a method evaluated as an image to support transient analysis on rotating machines In this work, they detect the presence of a signal with an SNR ≥ −22.9 dB. Thanh Tran and Jan Lundgren in [15] show a drilling fault diagnosis method based on scalogram and spectrogram of sound signals These authors state that in industry, the ability to detect damage or abnormal operation in machinery is very important; they do not show the performance of their method with a signal-to-noise ratio below zero. Researchers in [16] show a work on the application of the adaptive Wavelet transform for the diagnosis of gear failures using a filtered vibration signal These authors state that the scalogram is excellent for analyzing signals with a signal-to-noise ratio below zero.
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