×

One or two frequencies? The synchrosqueezing answers. (English) Zbl 1234.94018

Summary: The synchrosqueezed transform was proposed recently in [I. Daubechies, J. Lu and H.-T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool”, Appl. Comput. Harmon. Anal. 30, No. 2, 243–261 (2011; Zbl 1213.42133)] as an alternative to the empirical mode decomposition (EMD), to decompose composite signals into a sum of “modes” that each have well-defined instantaneous frequencies. This paper presents, for synchrosqueezing, a study similar to that in [G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers”, IEEE Trans. Signal Process. 56, No. 1, 85–95 (2008)] for EMD of how two signals with close frequencies are recognized and represented as such.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets

Citations:

Zbl 1213.42133
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1109/78.382394 · doi:10.1109/78.382394
[2] DOI: 10.1007/978-1-4612-0025-3_8 · doi:10.1007/978-1-4612-0025-3_8
[3] DOI: 10.1109/97.633772 · doi:10.1109/97.633772
[4] I. Daubechies and S. Maes, Wavelets in Medicine and Biology, eds. A. Aldroubi and M. Unser (CRC Press, Boca Raton, FL, 1996) pp. 527–546.
[5] DOI: 10.1098/rspa.1998.0193 · Zbl 0945.62093 · doi:10.1098/rspa.1998.0193
[6] Huang N. E., Rev. Geophys. 46 pp RG2006–
[7] DOI: 10.1142/S1793536909000096 · doi:10.1142/S1793536909000096
[8] DOI: 10.1109/TSP.2007.906771 · Zbl 1390.94382 · doi:10.1109/TSP.2007.906771
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.