Daubechies wavelet and scaling filters.

USAGE:

wavDaubechies( wavelet = ``d6", normalize = F )

DESCRIPTION:

Ingrid Daubechies, a noted pioneer in wavelet theory, has established a number of wavelet filter types, each with different mathematical properties. This function calculates the wavelet and scaling coefficients for a given filter type. The wavelet coefficients, h(k) for k = 0,...,L-1 where L is the filter length, are related to the scaling coefficients through the quadrature mirror filter (QMF) relation h(k) = (-1)^(k-L) g(L-1-k)

OPTIONAL ARGUMENTS:

wavelet
A character string denoting the filter type. Supported types include:

EXTREMAL PHASE (daublet): ``haar", ``d2", ``d4", ``d6", ``d8", ``d10", ``d12", ``d14", ``d16", ``d18", ``d20"

LEAST ASYMMETRIC (symmlet): ``s2",``s4", ``s6", ``s8", ``s10", ``s12", ``s14", ``s16", ``s18", ``s20"

BEST LOCALIZED: ``l2",``l4", ``l6", ``l14", ``l18", ``l20"

COIFLET: ``c6", ``c12", ``c18", ``c24", ``c30"

Default: ``s8".
normalize
A logical value. If TRUE, the filters are normalized by dividing each filter coefficient by the sqrt(2) (useful for maximum overlap wavelet transforms). If FALSE, no normalization is used. Default: TRUE.

VALUE:

result
An object of class WaveletDaubechies.

DETAILS:

Only relevant for Daubechies filter types. Inconsistent ordering of the coefficients in Daubechies' book was recognized and corrected by Percival (see references). The ``correct'' order is given here.

REFERENCES:

(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'', Cambridge University Press, 2000.

(2) I. Daubechies, ``Orthonormal Bases of Compactly Supported Wavelets'', Communications on Pure and, Applied Mathematics, 41, 909-96.

SEE ALSO:

, , , , , .

EXAMPLES:

   ## obtain Daubechies least asymmetric 8-tap filter set
   filters <- wavDaubechies( "s8", normalize = T )

   ## display filter information
   print( filters )

   ## plot the impulse responses
   plot( filters, type = "time" )

   ## plot the gain function
   plot( filters, type = "gain" )

   ## access the filter data
   wavelet <- filters$wavelet
   scaling <- filters$scaling