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

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  • Sun, Xiaoyun
  • Dang, Pei

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.

Suggested Citation

  • Sun, Xiaoyun & Dang, Pei, 2019. "Numerical stability of circular Hilbert transform and its application to signal decomposition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 357-373.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:357-373
    DOI: 10.1016/j.amc.2019.04.080
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