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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 25, issue 1
Nonlin. Processes Geophys., 25, 175–200, 2018
https://doi.org/10.5194/npg-25-175-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Nonlin. Processes Geophys., 25, 175–200, 2018
https://doi.org/10.5194/npg-25-175-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 05 Mar 2018

Research article | 05 Mar 2018

A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

Guillaume Lenoir and Michel Crucifix

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Revised manuscript accepted for NPG
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Cited articles

Berger, A. L.: Long-Term Variations of Caloric Insolation Resulting from the Earth's Orbital Elements, Quaternary Res., 9, 139–167, https://doi.org/10.1016/0033-5894(78)90064-9, 1978.
Berger, A. L., Loutre, M. F., and Mélice, J. L.: Instability of the atsronomical periods from 1.5 Myr BP to 0.5 Myr AP, Paleoclimates, 2, 239–280, 1998.
Brockwell, P. and Davis, R.: Time Series: Theory and Methods, Springer Series in Statistics, Second edn., Springer, New York, USA, 1991.
Carmona, R., Hwang, W., and Torresani, B.: Characterization of signals by the ridges of their wavelet transforms, IEEE T. Signal Proces., 45, 2586–2590, https://doi.org/10.1109/78.640725, 1997.
Carmona, R., Hwang, W., and Torresani, B.: Multiridge detection and time-frequency reconstruction, IEEE T. Signal Proces., 47, 480–492, https://doi.org/10.1109/78.740131, 1999.
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There is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework with the Morlet wavelet, based on the results of part I of this study. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.
There is so far no general framework for handling the continuous wavelet transform when the time...
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