dwt(x, wavelet="s8", n.levels=6, boundary=NULL,
    precondition=F, pdeg=0, pfrac=0, dual=F,
    analysis.filter=NULL, synthesis.filter=NULL)
as.dwt(x)
idwt(x)

x:

a vector or time series object. For as.dwt, x is an object of class "ptable". For idwt, x is an object of class "dwt".

wavelet:

a character string giving the name of the wavelet, e.g. "d4", "s8". See wavelet for a list of all available wavelet names. For user-provided filter, input the values in analysis.filter and synthesis.filter below.

n.levels:

a non-negative integer specifying number of multi-resolution levels. If n.levels is bigger than ml, where ml is the maximum possible level, then n.levels is set to ml and a warning message is given. The max.level function is used to compute ml.

boundary:

a character string giving the boundary rules, e.g. "periodic", "infinite", "zero". See details below for a list of available boundary rules.

precondition:

logical flag: for boundary="interval" only. If TRUE, then a preconditioning transform will be applied to the the data. The preconditioning transformation preserves the vanishing moments property when the DWT is applied to polynomial signals. See Cohen, Daubechies, and Vial (1993) for details.

pdeg:

for "infinite"only: degree of polynomial used for boundary extension.

pfrac:

for boundary="infinite"only: fraction of data used to fit a polynomial of degree pdeg.

dual:

logical flag indicating if dual filter is used for analysis instead of synthesis. This argument only applies for biorthogonal wavelets. See wavelet for details.

analysis.filter:

for user-defined analysis filter. See filter argument in wave.filter for details.

synthesis.filter:

for user-defined synthesis filter. See filter argument in wave.filter for details. When analysis.filter is provided, then the default synthesis.filter is also analysis.filter.

as.dwt coerces a ptable object to a dwt object.

idwt applies the inverse DWT to the transform coefficients to reconstruct the original signal.

• the original series is assumed to be periodic. Sample size must be divisible by 2^(n.levels).
• at each level, series is extended using a polynomial extrapolation of degree 0.
• at each level, series is extended using a polynomial extrapolation of degree 1.
• at each level, series is extended using a polynomial extrapolation of degree 1.
• at each level, the series is extended using zeros.
• the series is reflected (and then periodically extended). For perfect reconstruction, biorthogonal symmetric/antisymmetric wavelets are needed.
• uses Cohen, Daubechies and Vial's interval wavelets. Sample size must be divisible by 2^(n.levels). For wavelet="s4", "s6", "s8", "s10", "s12", "s14", "s16" only.
• the signal is padded using a polynomial (of degree pdeg) extension; a fraction (specified by pfrac) of data are used to fit two polynomial regression models, one for each end. For each crystal, extra coefficients (of maginitude O(length(filter))) are stored as left.pad and right.pad in order to recover all the coefficients (infinite number of them!).

The default boundary rule is set based on sample size, filter length in the following way: if n.levels can be achieved by "periodic" boundary rule (i.e. sample size is divisible by 2^n.levels), then the boundary is set to be "periodic"; otherwise, the boundary is set to be either "reflection" (for biorthogonal symmetric/anti-symmetric wavelets), or "zero".

All the default optional arguments can be reset using function wavelet.options. See wavelet.options for details.

Cohen, A., Daubechies, I. and Vial, P. (1993). Wavelets on the Interval and Fast Wavelet Transforms, Applied and Computational Harmonic Analysis, Vol 1, 54-81.

xx <- make.signal("doppler", 512, snr=5)   # a noisy doppler siganl
par(mfrow=c(2,2))
plot(xx, type="l", xlab="")
yy <- dwt(xx, wavelet="s8", boundary="periodic", n.levels=4)
plot(yy)

yy[c("d1","d2","d3")] <- 0     # set finer level coefficients 0
x2 <- reconstruct(yy)          # reconstructed doppler
plot(x2, type="l", xlab="")

yy[["d4"]][-(6:9)] <- 0        # assign 0's to all but the 6-9th coefficients
x3 <- reconstruct(yy)          # reconstructed doppler
plot(x3, type="l", xlab="", ylab="")