wmtsa (version 2.0-2)

wavShift: Shifts wavelet transform coefficients for approximate zero phase alignment

Description

If Daubechies symmlet or coiflet filters are used in forming a DWT or MODWT (ala wavDWT or wavMODWT, respectively), 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.

Usage

wavShift(x)

Arguments

x

an object of class wavTransform or wavBoundary.

Value

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

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.

I. Daubechies, Orthonormal Bases of Compactly Supported Wavelets, Communications on Pure and, Applied Mathematics, 41, 909--96.

See Also

wavZeroPhase, wavDWT, wavMODWT.

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, keep.series=TRUE)))