# sqcoefvec: Compute coefficients required for approximaing the wavelet... In hwwntest: Tests of White Noise using Wavelets

## Description

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

## Usage

 ```1 2``` ```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

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

`sqwd`, `sqndwd`, `sqndwdecomp`
 ```1 2 3 4``` ```# # This function is not really designed to be used by the casual user # tmp <- sqcoefvec(m0=2, filter.number=4) ```