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compgrot

Compute empirical shift for time ordered non-decimated transforms.

DESCRIPTION

Computes the empirical shift required for time-ordered non-decimated transform coefficients to bring them into time order.

USAGE

compgrot(J)

REQUIRED ARGUMENTS

J: The number of levels in the non-decimated transform where coefficients are to be time-aligned.

OPTIONAL ARGUMENTS

None.

VALUE

A vector containing the shifts that need to be applied to each scale level to return them to the correct time alignment.

There are J entries in the vector. The first entry corresponds to the shift required for the finest level coefficients (i.e. level J-1) and the last entry corresponds to the coarsest level (i.e. level 0). Entry j corresponds to the shift required for scale level J-j.

SIDE EFFECTS

None.

DETAILS

Time-ordered non-decimated transform coefficients when raw are not in exact time alignment due to the phase of the underlying wavelet. This function returns the shifts that are necessary to apply to each resolution level in the transform to bring back each set of time-ordered coefficients into time alignment. Note that the shifts returned are approximate shifts which work for any Daubechies wavelet. More accurate shifts can be computed using detailed knowledge of the particular wavelet used.

Each shift is "to the left". I.e. higher indexed coefficients should take the place of lower-indexed coefficients. Periodic boundaries are assumed.

This realignment is mentioned in Walden and Contreras Cristan, (1997) and Nason, Sapatinas and Sawczenko, (1998).

NOTE

GROT was the shop started by Reginald Perrin. Unfortunately, GROT stands for "Guy ROTation".

RELEASE

EXAMPLES

#
# Let's see how the resolution levels have to be shifted 
#
compgrot(4)
#[1]  2  6 15 31
#
# In other words. Scale level 3 needs to be shifted two units.
# Scale level 2 needs to be shifted 6 units
# Scale level 1 needs to be shifted 15 units
# Scale level 0 needs to be shifted 31 units.