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 ) ) )