Numerical stability of circular Hilbert transform and its application to signal decomposition

Xiaoyun Sun and Pei Dang

Applied Mathematics and Computation, 2019, vol. 359, issue C, 357-373

Abstract: In this paper, we propose a novel method of computing Hilbert transform based on the mechanical quadrature method. Experiments show that the method outperforms the library function ‘hilbert’ in Matlab when the values of functions being handled are very large or approach to infinity, that is a problem we have to deal with when we compute, for instance, outer functions. As an application, we use the method to obtain the unwinding series of signals, which is a positive frequency decomposition of signals and is dependent of extraction of outer functions involving computation of Hilbert transform. The experimental results show better stability. Then, we give the transient time frequency distribution of the unwinding series of signals. Finally, experiments of noisy signals are given, and the results show that the introduced method can well resist some disturbance.

Keywords: Hilbert transform; Mechanical quadrature; Unwinding series; Inner and outer functions; Transient time-frequency distribution (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:359:y:2019:i:c:p:357-373

DOI: 10.1016/j.amc.2019.04.080

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