Vakmanʼs problem and the extension of Hilbert transform

Applied and Computational Harmonic Analysis

Volumn 34, Issue 2, 2013, Pages 308-316

  Huang, Jianfeng ^a   Wang, Yang ^b   Yang, Lihua ^a  

^a SUN YAT SEN UNIVERSITY   (China)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Almost periodic function; Analytic signal method; BMO; Hilbert transform; Instantaneous frequency; Vakmans argument

Indexed keywords

FUNCTIONAL ANALYSIS; HILBERT SPACES;

ALMOST PERIODIC FUNCTION; ANALYTIC SIGNALS; HILBERT TRANSFORM; INSTANTANEOUS FREQUENCY; VAKMANS ARGUMENT;

MATHEMATICAL TRANSFORMATIONS;

EID: 84872314783     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2012.08.009     Document Type: Letter

References (16)

1. N.K. Bary A Treatise on Trigonometric Series, vols. I, II authorized translation by Margaret F. Mullins 1964 Pergamon Press New York
2. E. Bedrosian A product theorem for Hilbert transform Proc. IEEE 51 1963 868 869
3. P.L. Butzer, and R.J. Nessel Fourier Analysis and Approximation, vol. 1 1971 Academic Press New York
4. C. Corduneanu Almost Periodic Oscillations and Waves 2009 Springer Science + Business Media, LLC
5. G.B. Folland Real Analysis 1984 John Wiley & Sons Inc.
6. D. Gabor Theory of communication J. Inst. Electr. Eng. 93 1946 429 457
7. J.B. Garnett Bounded Analytic Functions 1981 Academic Press
8. L. Grafakos Modern Fourier Analysis 2009 Springer Science + Business Media, LLC
9. 2 (R) Int. J. Comput. Math. 88 3 2011 545 554
10. Y. Katznelson An Introduction to Harmonic Analysis 3rd edition 2004 Cambridge University Press
11. J.N. Pandey The Hilbert transform of periodic distributions Integral Transforms Spec. Funct. 5 1-2 1997 117 142
12. M.A. Pinsky Introduction to Fourier Analysis and Wavelets 2002 Brooks/Cole Pacific Grove, CA
13. L. Tan, L. Yang, and D. Huang Construction of periodic analytic signals satisfying the circular Bedrosian identity IMA J. Appl. Math. 75 2 2010 246 256 http://dx.doi.org/10.1093/imamat/hxq001
14. D. Vakman On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency IEEE Trans. Signal Process. 44 4 1996 791 797
15. D.E. Vakman On the definition of concepts of amplitude, phase and instantaneous frequency of a signal Radio Eng. Electron. Phys. 17 5 1972 754 759
16. Y. Xu, and D. Yan The Bedrosian identity for the Hilbert transform of product functions Proc. Amer. Math. Soc. 134 9 2006 2719 2728