Compute coefficients required for approximaing the wavelet transform using the square of wavelets.

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Description

Essentially, part of a method for computing a wavelet-like transform using the squares of wavelets rather than the wavelets themselves.

Usage

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sqcoefvec(m0, filter.number = 10, family = "DaubLeAsymm",
	resolution = 4096, stop.on.error = FALSE, plot.it = FALSE)

Arguments

m0

The number of scales finer than the square wavelet being approximated. Usually, 2 or 3 is enough.

filter.number

Number of vanishing moments of underlying wavelet.

family

Family of underlying wavelet

resolution

Function values of the wavelet itself are generated by a high-resolution approximation. This argument specifies exactly how many values.

stop.on.error

This argument is supplied to the integrate function which performs numerical integration within this code.

plot.it

Plots showing the approximation are plotted.

Details

The idea is that the square of a wavelet (the square wavelet) is approximated by wavelets at a finer scale. The argument m0 controls how many levels below the original scale are used. Essentially, this function computes a representation of the original square wavelet in terms of finer scale wavelets. Hence, when a decomposition of another function with respect to the square wavelets is required, one can compute the representation with respect to a regular wavelet decomposition and then apply the wavelet to square wavelet transform to turn it into a square wavelet representation.

This idea originally used for performing ‘powers of wavelets’ transforms in Herrick (2000) and Barber, Nason and Silverman (2002) and for the mod-wavelets is described in Fryzlewicz, Nason and von Sachs (2008).

Value

A list with the following components:

ll

Vector containing integers between the lower and upper limit of the wavelets required at the finer scale.

ecoef

The appropriate coefficients that approximate the mod wavelet at the finer scale.

m0

The number of scales finer below the scale that the function is at

filter.number

The wavelet filter number used

family

The wavelet family used

ecode

An error code, if zero then ok, otherwise returns 1

ians

The actual return values from the internal call to the integrate function

Author(s)

Guy Nason

References

Barber, S., Nason, G.P. and Silverman, B.W. (2002) Posterior probability intervals for wavelet thresholding. J. R. Statist. Soc. B, 64, 189-206.

Fryzlewicz, P., Nason, G.P. and von Sachs, R. (2008) A wavelet-Fisz approach to spectrum estimation. J. Time Ser. Anal., 29, 868-880.

Herrick, D.R.M. (2000) Wavelet Methods for Curve Estimation, PhD thesis, University of Bristol, U.K.

Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. http://dx.doi.org/10.1002/sta4.69

See Also

sqwd, sqndwd, sqndwdecomp

Examples

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#
# This function is not really designed to be used by the casual user
#
tmp <- sqcoefvec(m0=2, filter.number=4)