Zero phase shift factors for Daubechies symmlet and coiflet filters.

USAGE:

wavZeroPhase( wavelet = ``s8", levels = 1:3 )

DESCRIPTION:

Daubechies coiflet and symmlet filters are approximate linear phase filters. Consequently, the wavelet and scaling coefficients of the DWT (using convolution style filtering), MODWT, DWPT, and MODWPT can be circularly shifted for approximate zero phase alignment with the original time series. This function calculates the circular shift factors needed to bring the wavelet and scaling coefficients to approximate zero phase.

OPTIONAL ARGUMENTS:

wavelet
A character string denoting the filter type. See wavDaubechies for details. Default: ``s8".
levels
An integer vector containing the decomposition levels. Default: 1:3.

VALUE:

result
A list containing the shifts for each crystal of a DWT, DWPT, MODWT, and MODWPT for the specified decomposition levels. A negative shift factor implies an advance (circular shift to the left) of the wavelet transform crystals.

DETAILS:

Only relevant for DWT, MODWT, DWPT, and MODWPT definitions as given in the above reference and is valid only for Daubechies symmlet and coiflet filters.

REFERENCES:

(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'', Cambridge University Press, 2000.

SEE ALSO:

, , , , , .

EXAMPLES:

   ## calculate the zero phase
   ## shift factors for Daubechies coiflet
   ## 12-tap filters for levels 2 and 4.
   wavZeroPhase( wavelet = "c12", levels = c(2,4) )