The Bedrosian identity for Hp functions

Journal of Mathematical Analysis and Applications

Volumn 345, Issue 2, 2008, Pages 975-984

  Yang, Lihua ^a   Zhang, Haizhang ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b SYRACUSE UNIVERSITY   (United States)

Author keywords

Bedrosian theorem; Hilbert transform

Indexed keywords

EID: 44649195023     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.05.005     Document Type: Article

References (27)

1. Bedrosian E. A product theorem for Hilbert transforms. Proc. IEEE 51 (1963) 868-869
2. Brown J.L. Analytic signals and product theorems for Hilbert transforms. IEEE Trans. Circuits Syst. CAS-21 (1974) 790-792
3. Brown J.L. A Hilbert transform product theorem. Proc. IEEE 74 (1986) 520-521
4. Butzer P.L., and Nessel R.J. Fourier Analysis and Approximation. Volume 1: One-dimensional Theory. Pure Appl. Math. vol. 40 (1971), Academic Press, New York
5. Cohen L. Time-Frequency Analysis: Theory and Applications (1995), Prentice Hall, Englewood Cliffs, NJ
6. Donoghue W.F. Distributions and Fourier Transforms (1969), Academic Press, New York
7. Garnett J.B. Bounded Analytic Functions (1981), Academic Press, New York
8. Gasquet C., and Witomski P. Fourier Analysis and Applications (1999), Springer-Verlag, New York
9. Huang N.E., et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 454 (1998) 903-995
10. p Spaces. second ed. (1998), Cambridge University Press, Cambridge
11. Li B., and Guo L. Riesz transformations of distributions and a generalized Hardy space. Approx. Theory Appl. 5 (1989) 1-17
12. Lions J.L. Support dans la transformation de Laplace. J. Anal. Math. 2 (1952/1953) 369-380
13. Nuttall A.H., and Bedrosian E. On the quadrature approximation to the Hilbert transform of modulated signals. Proc. IEEE 54 (1966) 1458-1459
14. Picibono B. On instantaneous amplitude and phase of signals. IEEE Trans. Signal Process. 45 (1997) 552-560
15. Qian T., Chen Q., and Li L. Analytic unit quadrature signals with nonlinear phase. Phys. D 203 (2005) 80-87
16. T. Qian, R. Wang, Y. Xu, H. Zhang, Orthonormal bases with nonlinear phases, J. Fourier Anal. Appl., submitted for publication
17. T. Qian, Y. Xu, D. Yan, L. Yan, B. Yu, Fourier spectrum characterization of Hardy spaces and applications, Proc. Amer. Math. Soc., in press
18. Radjavi H., and Rosenthal P. Invariant Subspaces. second ed. (2003), Dover Publications, Inc., Mineola, New York
19. Stein E.M. Harmonic Analysis (1993), Princeton University Press, Princeton, NJ
20. L. Tan, L. Yang, D. Huang, Necessary and sufficient conditions for the Bedrosian identity, J. Integral Equations Appl., in press
21. Titchmarsh E.C. The zeros of certain integral functions. Proc. London Math. Soc. s2-25 (1926) 283-302
22. Vakman D. On the definition of concepts of amplitude, phase and instantaneous frequency of a signal. Radio Eng. Electron. Phys. 17 (1972) 754-759
23. Vakman D. On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency. IEEE Trans. Signal Process. 44 (1996) 791-797
24. Venouziou M., and Zhang H. Characterizing the Hilbert transform by the Bedrosian theorem. J. Math. Anal. Appl. 338 (2008) 1477-1481
25. Xu Y., and Yan D. The Bedrosian identity for the Hilbert transform of product functions. Proc. Amer. Math. Soc. 134 (2006) 2719-2728
26. Y. Xu, H. Zhang, Recent mathematical developments on empirical mode decomposition, Advances in Adaptive Data Analysis: Theory and Applications, in press
27. B. Yu, H. Zhang, The Bedrosian identity and homogeneous semi-convolution equations, J. Integral Equations Appl., in press