wavDaubechies {wmtsa} | R Documentation |
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)
wavDaubechies(wavelet="s8", normalized=TRUE)
normalized |
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 . |
wavelet |
a character string denoting the filter type. Supported types include:
Default: "s8" . |
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.
an object of class wavDaubechies
.
Usage: plot(x, type="time")
wavDaubechies
object."time"
, "gain"
, and "phase"
for an
impulse response, squared gain, and phase plot, respectively.
Default: "time"
.Usage: print(x, verbose=TRUE)
wavDaubechies
object.TRUE
, the filter coefficients
are also printed. Default: TRUE
.
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
I. Daubechies, Orthonormal Bases of Compactly Supported Wavelets, Communications on Pure and, Applied Mathematics, 41, 909–96.
wavGain
, wavDWT
, wavMODWT
, wavMODWPT
.
## obtain Daubechies least asymmetric 8-tap filter ## set filters <- wavDaubechies("s8", normalize=TRUE) ## plot the impulse responses plot(filters, type="time") ## plot the gain function plot(filters, type="gain")