What question did this study set out to answer?

To outline the mathematical foundations of the continuous wavelet transform and demonstrate its utility in dissecting multiscale, non-stationary phenomena across theoretical models and real-world climate records.

November 30, 1996Physics-Uspekhi

Wavelet analysis: basic theory and some applications

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Authors

NAN.M. Astaf'evaSpace Research Institute

Discussion

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Implication

Time-series analysis reveals multiscale periodicities and leading Northern Hemisphere warming trends in climate records, highlighting the value of localized wavelet transforms.

Key Points

To outline the mathematical foundations of the continuous wavelet transform and demonstrate its utility in dissecting multiscale, non-stationary phenomena across theoretical models and real-world climate records.
Formulated one-dimensional wavelet transforms using analyzing functions localized simultaneously across time and frequency domains.
Applied the wavelet transform framework to synthetic test series (harmonic, fractal, and singular functions) alongside meteorological datasets, including the Southern Oscillation index and global and hemispheric temperature records.
Wavelet decomposition of the Southern Oscillation index and El Niño events identified concurrent regular periodicities, transient localized cycles, and multiscale self-similar structures.
Global and hemispheric temperature analyses demonstrated structurally similar behavior, with Northern Hemisphere warming exhibiting a stronger magnitude and leading the Southern Hemisphere chronologically.

Cite This Study

N.M. Astaf'eva (1996) studied this question.

synapsesocial.com/papers/6a013151831589f3542e075f https://doi.org/10.1070/pu1996v039n11abeh000177

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November 30, 1996Physics-Uspekhi

Wavelet analysis: basic theory and some applications

View Full Paper

Ask AI

Bookmark

Authors

NAN.M. Astaf'evaSpace Research Institute

Discussion

Member takes

Implication

Time-series analysis reveals multiscale periodicities and leading Northern Hemisphere warming trends in climate records, highlighting the value of localized wavelet transforms.

Key Points

To outline the mathematical foundations of the continuous wavelet transform and demonstrate its utility in dissecting multiscale, non-stationary phenomena across theoretical models and real-world climate records.
Formulated one-dimensional wavelet transforms using analyzing functions localized simultaneously across time and frequency domains.
Applied the wavelet transform framework to synthetic test series (harmonic, fractal, and singular functions) alongside meteorological datasets, including the Southern Oscillation index and global and hemispheric temperature records.
Wavelet decomposition of the Southern Oscillation index and El Niño events identified concurrent regular periodicities, transient localized cycles, and multiscale self-similar structures.
Global and hemispheric temperature analyses demonstrated structurally similar behavior, with Northern Hemisphere warming exhibiting a stronger magnitude and leading the Southern Hemisphere chronologically.

Cite This Study

N.M. Astaf'eva (1996) studied this question.

synapsesocial.com/papers/6a013151831589f3542e075f https://doi.org/10.1070/pu1996v039n11abeh000177

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