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A NOTE ON ANALYTIC SIGNALS WITH NONLINEAR PHASE

SHOUYIN CHEN

School of Business, Hubei University, Wuhan 430062, P. R. China

https://doi.org/10.1142/S0219691309003161Cited by:2 (Source: Crossref)

Abstract

Instantaneous frequency, defined as the derivative of the phase of a complex analytic representation of the signal, is a basic concept and plays an important role in communication and information processing. It is not unusual to expect that the instantaneous frequency of an analytic signal is nonnegative. In this note, we exhibit new families of analytic signals with band-limited amplitudes and positive nonlinear instantaneous frequencies. The structures of analytic signals with band-limited amplitude and rational as well as linear plus periodic instantaneous frequencies have been analyzed.

Keywords:

AMSC: 94A12, 65R10

References

E. Bedrosian, Proc. IEEE 51, 868 (1963), DOI: 10.1109/PROC.1963.2308. Web of Science, Google Scholar
B. Boashash, Proc. IEEE 80, 520 (1992), DOI: 10.1109/5.135376. Web of Science, Google Scholar
B. Boashash, Proc. IEEE 80, 540 (1992), DOI: 10.1109/5.135378. Web of Science, Google Scholar
Q. H. Chen, L. Q. Li and T. Qian, Int. J. Wavelets Multiresolut. Inf. Process. 3, 465 (2005), DOI: 10.1142/S0219691305000968. Link, Web of Science, Google Scholar
Q. H. Chen, L. Q. Li and T. Qian, Phys. D 221, 1 (2006), DOI: 10.1016/j.physd.2006.06.013. Web of Science, Google Scholar
L. Cohen , Time-Frequency Analysis ( Prentice-Hall , 1995 ) . Google Scholar
M. I. Doroslovacki, Signal Process. 83, 655 (2003), DOI: 10.1016/S0165-1684(02)00483-8. Web of Science, Google Scholar
Y. X. Fu and L. Q. Li, Nonlinear Anal. 68, 2431 (2008). Web of Science, Google Scholar
D. Gabor, J. Inst. Elect. Eng. 93, 429 (1946). Google Scholar
J. B. Garnett , Bounded Analytic Functions ( Academic Press , Boston , 1987 ) . Google Scholar
S. L. Hahn , Hilbert Transforms in Signal Processing ( Artech House , 1996 ) . Google Scholar
H. Li, L. Q. Li and Y. Y. Tang, Int. J. Wavelets Multiresolut. Inf. Process. 5, 941 (2007), DOI: 10.1142/S0219691307002130. Link, Web of Science, Google Scholar
A. H. Nuttall and E. Bedrosian, Proc. IEEE (Letters) 54, 1458 (1966). Web of Science, Google Scholar
B. Picinbono, IEEE Trans. Signal Process. 45, 552 (1997), DOI: 10.1109/78.558469. Web of Science, Google Scholar
T. Qian, J. Integral Equations Appl. 17, 159 (2005), DOI: 10.1216/jiea/1181075323. Web of Science, Google Scholar
T. Qian, J. Math. Anal. Appl. 314, 526 (2006), DOI: 10.1016/j.jmaa.2005.04.003. Web of Science, Google Scholar
T. Qian, Math. Methods Appl. Sci. 29, 1187 (2006), DOI: 10.1002/mma.721. Web of Science, Google Scholar
T. Qian, Q. H. Chen and L. Q. Li, Phys. D 203, 80 (2005), DOI: 10.1016/j.physd.2005.03.005. Web of Science, Google Scholar
T. Qian, L. M. Zhang and H. Li, Int. J. Wavelets Multiresolut. Inf. Process. 6, 353 (2008), DOI: 10.1142/S0219691308002392. Link, Web of Science, Google Scholar
D. E. Vakman, IEEE Trans. Signal Process. 44, 791 (1996), DOI: 10.1109/78.492532. Web of Science, Google Scholar
D. E. Vakman and L. A. Vainshtein, Sov. Phys. Usp. 20, 1002 (1978), DOI: 10.1070/PU1977v020n12ABEH005479. Google Scholar
X. G. Xia and L. Cohen, On analytic signals with nonnegative instantaneous frequencies, Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing3 (IEEE Press, 1999) pp. 1329–1332. Google Scholar