Create Wavelet/Wavelet Packet Function
DESCRIPTION:
Create wavelet or wavelet packet functions.
USAGE: 
wavelet(wavelet="s8", mother=T, level=0, shift=0, dual=F,
        filter=NULL, filter.start=0)
wavelet.packet(wavelet="s8", oscillation=0, level=0, shift=0,
               dual=F, filter=NULL, filter.start=0)
OPTIONAL ARGUMENTS:
wavelet:
character string indicating the wavelet name; must be one of the wavelet names listed in the details below.
mother:
logical flag indicating whether the mother or father wavelet is requested. If TRUE, the mother wavelet is returned. The default is TRUE.
oscillation:
for wavelet.packet only. A natural number corresponding to the number of zero crossings. For the haar wavelet, this correspondence is exact. A value of 0 indicates the father wavelet (scaling function); a value of 1 indicates the mother wavelet. The default is 0.
level:
integer giving the scaling parameter. A wavelet or wavelet packet has scale 2^level, corresponding to the resolution level; see details below. The default is 0.
shift:
integer giving the translation shift parameter. A wavelet or wavelet packet has location shift*2^level; see details below. The default is 0.
dual:
logical flag indicating if the wavelet packet function is from the dual filter space. The default is FALSE.
filter:
for user defined filter only. Must be a vector or a list of two vectors. See wave.filter for details.
filter.start:
an integer giving filter starting index. It determines the support of the associated wavelet.
VALUE:
wavelet() creates an object of class wavelet, inheriting from wavelet.packet; wavelet.packet() creates an object of class wavelet.packet. See wavelet.packet.object for the structure of these objects.
DETAILS:
Wavelets are fundamental building block "bump" functions. There are two types of wavelet functions: father wavelets (also known as scaling functions) and mother wavelets. The available orthogonal wavelets are

The available biorthogonal wavelets are:

Refer to Daubechies (1992) or the chapter "Wavelet Analysis of 1-D Signals" of the S+WAVELETS User's Manual.

Wavelet packet functions are a generalization of wavelet functions. Wavelet packet functions are still localized in time, but offer more flexibility than wavelets in representing different types of signals. In particular, wavelet packets are better at representing signals that exhibit oscillatory or periodic behavior.

See the printed help file for the general form of a wavelet packet function.

Refer to Wickerhauser (1994) or the chapter "Wavelet Packet Analysis" of the S+WAVELETS User's Manual for more details.

REFERENCES:
Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.

Wickerhauser, M. V. (1994). Adapted Wavelet Analysis -- from theory to software.

SEE ALSO:
fourier.transform.plot , plot.wavelet.packet , support , wavelet.packet.object .
EXAMPLES: 
par(mfrow=c(2,2))
plot(wavelet("d4", mother=F))
plot(wavelet("s8", mother=T, level=3))
plot(wavelet("bs2.4", mother=T, dual=F, level=2))
plot(wavelet("vs2", mother=T, dual=F, level=1, shift=1))


plot(wavelet.packet(wavelet="s8", oscillation=1, level=0))
plot(wavelet.packet("s8", oscillation=1, level=3))
plot(wavelet.packet(wavelet="s8", oscillation=3, level=0))
plot(wavelet.packet("s8", oscillation=4, level=3))