Essentially, part of a method for computing a wavelet-like transform using the squares of wavelets rather than the wavelets themselves.
sqcoefvec(m0, filter.number = 10, family = "DaubLeAsymm",
resolution = 4096, stop.on.error = FALSE, plot.it = FALSE)A list with the following components:
Vector containing integers between the lower and upper limit of the wavelets required at the finer scale.
The appropriate coefficients that approximate the mod wavelet at the finer scale.
The number of scales finer below the scale that the function is at
The wavelet filter number used
The wavelet family used
An error code, if zero then ok, otherwise returns 1
The actual return values from the internal call to the
integrate function
The number of scales finer than the square wavelet being approximated. Usually, 2 or 3 is enough.
Number of vanishing moments of underlying wavelet.
Family of underlying wavelet
Function values of the wavelet itself are generated by a high-resolution approximation. This argument specifies exactly how many values.
This argument is supplied to the integrate
function which performs numerical integration within this code.
Plots showing the approximation are plotted.
Guy Nason
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).
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. tools:::Rd_expr_doi("10.1002/sta4.69")
sqwd, sqndwd,
sqndwdecomp
#
# This function is not really designed to be used by the casual user
#
tmp <- sqcoefvec(m0=2, filter.number=4)
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