Compute coefficients required for approximaing the wavelet transform using the square of wavelets.
Description
Essentially, part of a method for computing a waveletlike transform using the squares of wavelets rather than the wavelets themselves.
Usage
1 2 
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 highresolution approximation. This argument specifies exactly how many values. 
stop.on.error 
This argument is supplied to the 
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 modwavelets 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

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, 189206.
Fryzlewicz, P., Nason, G.P. and von Sachs, R. (2008) A waveletFisz approach to spectrum estimation. J. Time Ser. Anal., 29, 868880.
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, 351362. http://dx.doi.org/10.1002/sta4.69
See Also
sqwd
, sqndwd
,
sqndwdecomp
Examples
1 2 3 4  #
# This function is not really designed to be used by the casual user
#
tmp < sqcoefvec(m0=2, filter.number=4)
