Analytic unit quadrature signals with nonlinear phase. (English) Zbl 1070.94504

Qian, Tao; Chen, Qiuhui; Li, Luoqing

Physica D 203, No. 1-2, 80-87 (2005).

Summary: The notion of intrinsic mode functions (IMFs) in the algorithm of Hilbert-Huang transform (HHT) [N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 454, 903–995 (1998; Zbl 0945.62093)] is essentially an engineering description in relation to mono-components of nonlinear and non-stationary signals. In this note we prove a version of Bedrosian’s theorem on the unit circle. We give a sufficient condition together with an example for nonlinear phases \(\theta(t)\) that make the unit quadrature signals \(e^{i\theta(t)}\) analytic. We also establish a corresponding relationship between the periodic and non-periodic signals on the whole time range.

MSC:

94A12	Signal theory (characterization, reconstruction, filtering, etc.)
62M15	Inference from stochastic processes and spectral analysis
44A15	Special integral transforms (Legendre, Hilbert, etc.)

Keywords:

Hilbert-Huang transform; Nonlinear and non-stationary signal; Möbius transform; Bedrosian’s theorem

Citations:

Zbl 0945.62093

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