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

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.


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


Zbl 0945.62093
Full Text: DOI


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