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accessD.wd

Get detail (mother wavelet) coefficients from wavelet object (wd).

DESCRIPTION

This function extracts and returns a vector of mother wavelet coefficients, corresponding to a particular resolution level, from a wd wavelet decomposition object.

The pyramid of coefficients in a wavelet decomposition (returned from the wd function, say) are packed into a single vector in WaveThresh.

USAGE

accessD.wd(wdobj, level, boundary=F, aspect="Identity")

REQUIRED ARGUMENTS

wdobj: Wavelet decomposition object from which you wish to extract the mother wavelet coefficients.
level: The resolution level at which you wish to extract coefficients.

OPTIONAL ARGUMENTS

boundary: some methods of wavelet transform computation handle the boundaries by keeping some extra bookkeeping coefficients at either end of a resolution level. If this argument is T then these bookkeeping coefficients are returned when the mother wavelets are returned. Otherwise, if F, these coefficients are not returned.
aspect: The aspect argument permits the user to supply a function to modify the returned coefficients. The function is applied to the vector of coefficients before it is returned. This can be useful, say, with the complex DWT where you could supply aspect="Mod" if you wanted to return the modulus of the coefficients at a given resolution level. The default argument, "Identity", ensures that the coefficients are not modified before returning.

VALUE

A vector containing the mother wavelet coefficients at the required resolution level (the coefficients might have been modified depending on the value of the aspect argument).

DETAILS

The need for this function is a consequence of the pyramidal structure of Mallat's algorithm and the memory efficiency gain achieved by storing the pyramid as a linear vector. AccessD obtains information about where the smoothed data appears from the fl.dbase component of an wd object, in particular the array

fl.dbase$first.last.d

which gives a complete specification of index numbers and offsets for

wd.object$D.

Note that this function is a method for the generic function accessD.

Note also that this function only retrieves information from wd class objects. To insert coefficients into wd objects you have to use the putD function (or more precisely, the putD.wd method).

RELEASE

REFERENCES

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 11, 674--693.

Nason, G. P. and Silverman, B. W. (1994). The discrete wavelet transform in S. Journal of Computational and Graphical Statistics, 3, 163--191.

EXAMPLES

#
# Get the 4th resolution level of wavelet coefficients. 
#
> accessD(wd(data), level=4)
#
# Get the absolute value of the 7th level of complex wavelet coefficients
#
> my.wd <- wd(data, filter.number=3, family="Lawton")
> accessD(my.wd, level=7, aspect="Mod")