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 )