The gain functions for Daubechies wavelet and scaling filters.

USAGE:

wavGain( wavelet = ``s20", n.levels = 5, normalize = T )

DESCRIPTION:

Given g and h are the impulse responses for the scaling and wavelet filters, respectively, and G(1,1f) and H(1,f) are their corresponding gain functions, then the gain functions for decomposition level j > 1 are calculated using the recursive algorithm:

H(j,f) = H(1, 2^(j-1)*f) * G(j-1, f),

G(j,f) = G(1, 2^(j-1)*f) * G(j-1,f).

OPTIONAL ARGUMENTS:

wavelet
A character string denoting the filter type. See wavDaubechies for details. Default: ``s8".
n.levels
The number of decomposition levels. Default: 5.
n.fft
The number of Fourier coefficients to use in approximating the gain functions. Default: 1024.
normalize
A boolean value. If TRUE, the filters are normalized by dividing each filter coefficient by the sqrt(2) (used for maximal overlap wavelet transforms). If FALSE, no normalization is used. Default: TRUE.

VALUE:

result
An object of class WaveletGain.

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:

   ## approximate the gain functions for the
   ## normalized Daubechies least
   ## asymmetric 20-tap filters for levels 1,...,5
   ## using a 1024 Fourier frequencies
   result <- wavGain( wavelet = "s20", n.levels = 5,
   + norm = T )

   ## plot the results
   plot( result )