Shifts wavelet transform coefficients for approximate zero phase alignment.
USAGE:
wavShift( x )
DESCRIPTION:
If Daubechies symmlets or coiflets are used in a DWT, MODWT, DWPT, or MODWPT,
then the transform coefficients can be circularly rotated so that they are
approximately aligned (in time) with events of the original time series. An
appropriate shift of the coefficients (generated by approximate linear phase
filter operations) is approximately equivalent to using zero phase filters in
the wavelet transform.
REQUIRED ARGUMENTS:
x
An object of class WaveletTransform,WaveletBoundary or WaveletPacket.
VALUE:
result
An object of the same class as the input with the transform coefficients
adjusted to approximate zero phase filtering operations.
DETAILS:
Only relevant for transforms calculated using Daubechies coiflet and symmlet
filters. A second application of wavShift to the same input object will result
in the original input object, i.e. without any imposed shift in the transform
coefficients.
REFERENCES:
(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'',
Cambridge University Press, 2000.
(2) I. Daubechies, ``Orthonormal Bases of Compactly Supported Wavelets'',
Communications on Pure and, Applied Mathematics, 41, 909-96.
SEE ALSO:
,
,
,
,
,
.
EXAMPLES:
## plot the zero phase shifted MODWT of a
## linear chirp sequence
linchirp <- make.signal( "linchirp", n = 1024 )
plot( wavShift( wavMODWT( linchirp, wavelet = "s8",
+ n.levels = 4 ) ) )