## 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.

### MSC:

 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
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### References:

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