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   -> Volume 6, Issue 3


Preprint: Undecimated wavelet packet transform
 
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a.walden@ic.ac.uk (A Walden)
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PostPosted: Mon Mar 03, 1997 2:31 pm    
Subject: Preprint: Undecimated wavelet packet transform
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#8 Preprint: Undecimated wavelet packet transform

The following preprint is available via WWW at:
http://www.ma.ic.ac.uk/statistics/links/atw.link/phase-corrected-TR-97-03.ps

Title: The phase-corrected undecimated discrete wavelet packet transform
and the recurrence of high latitude interplanetary shock waves.

[Imperial College of Science, Technology and Medicine, Statistics Section
Technical report TR-97-03, February 1997.]

Authors: Andrew T. Walden and Alberto Contreras Cristan

Abstract: We develop and apply advanced time-frequency methodology to
examine the recurrence time between shock waves identified in a
non-stationary time series of hourly-averaged southern hemisphere
solar magnetic field magnitude data acquired by the Ulysses
spacecraft. The discrete cyclic filtering steps of the maximal overlap
discrete wavelet packet transform (MODWPT) are fully explained. Energy
preservation is proven. With filter coefficients chosen from
Daubechies least asymmetric class, the optimum time shifts to apply to
ensure approximate zero phase filtering at every level of the MODWPT
are studied, and applied to the wavelet packet coefficients to give
phase-corrections which ensure alignment with the original time
series. Also the time series values at each time are decomposed into
details associated with each frequency band, and these line up
perfectly with features in the original time series since the details
are shown to arise through exact zero phase filtering. We carry out a
level 4 phase-corrected MODWPT of the Ulysses magnetic field data, and
show that the recurrence times of the shock waves previously
determined via manual pattern-matching on the raw data match those
times in the time-frequency plot where a broadband spectrum is
obtained; in other words, the phase-corrected MODWPT provides an
approach to picking the location of complicated events. Furthermore,
the phase-corrected MODWPT time-frequency plot strongly suggests that
the first shock wave is a composite of two events,
possibly one associated with a corotating interaction region, and one due
to a coronal mass ejection. This might explain why the first shock wave has
been differently classified in recent studies.
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