Calculate the detail sequences for wavelet transform crystals

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Description

Let W(j,n) be a discrete wavelet packet crystal where j is the decomposition level and n is the oscillation index. The detail sequence D(j,t) is formed (essentially) by reconstructing the transform after zeroing out all other crystals except W(j,n). The wavMRD function calculates the details for a DWT and MODWT in an optimized way.

Usage

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wavMRD(x, level=NULL, osc=NULL)

Arguments

x

an object of class wavTransform.

level

an integer (vector) containing the decomposition level(s) corresponding to the crystal(s) to be decomposed. Default: If the input is of class wavTransform, then the default is to return the details at all levels of the transform, i.e., a full multiresolution decomposition.

osc

an integer (vector) containing the oscillation indices corresponding to the crystal(s) to be decomposed. Default: the default values are coordinated with that of the level argument.

Value

an object of class WaveletMRD.

S3 METHODS

[

single level data access.

Usage: x["D2"] or x["S4"]

Access a subset of wavelet transform details/smooth.

[<-

single level data replacement method.

Usage: x["D2"] <- 1:4

Replace an entire wavelet transform details/smooth with explicitly defined coefficients.

[[

double level data access.

Usage: x[["D2"]] or x[[2]]

Returns a vector of wavelet transform detail/smooth coefficients corresponding to the specified crystal.

as.matrix

transforms the list of wavelet transform details/smooth coefficients into a single-column matrix whose row names identify the transform coefficient, e.g., D4(3) is the third coefficient of the D4 detail.

Usage: as.matrix(x)

boxplot

plots a boxplot for each wavelet transform detail/smooth.

Usage: boxplot(x)

crystal.names

return the crystal names for each wavelet transform detail/smooth.

Usage: crystal.names(x)

plot

plot a stack plot of the discrete wavelet transform details/smooth. Usage: plot(x, n.top=15, vgap=.05, col=1, show.sum=TRUE, add=FALSE, ...)

x

A wavMRD object.

n.top

An integer defining the (maximum) number of top-most energetic crystals to plot. Default: 15.

sort.energy

A logical value. If TRUE, the crystals are sorted in the display from the most energetic (top) to the least energetic (bottom) of the specified n.top crystals. Default: FALSE.

vgap

A numeric scalar defining the vertical gap between plots expressed as a fraction of the maximum value of the details/smooth that are plotted. Default: 0.05.

col

An integer or vecto rof integers deining the color index to apply to each detail/smooth line plot. Default: 1.

show.sum

A logical value. If TRUE, a plot of the sum of all details/smooth is also plotted. Default: TRUE.

add

A logical value. If TRUE, the plot is added to the current plot layout without a frame ejection. Default: FALSE.

...

Additional arguments to be sent to the plot routine.

print

print the wavelet transform details/smooth object. Usage: print(x)

reconstruct

reconstruct/synthesize/invert the wavelet transform details/smooth. Usage: reconstruct(x)

If the transform coefficients were not modified, the original time series will be returned (+/- some numerical noise).

summary

provide a statistical summary of the wavelet transform details/smooth object. Usage: z <- summary(x); print(z)

wavStackPlot

stack plot of the wavelet transform details/smooth. Usage: wavStackPlot(x)

References

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.

See Also

wavMRDSum, reconstruct, wavDWT, wavMODWT.

Examples

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## calculate various wavelet transforms of the 
## first difference of a linear chirp sequence 
x <- make.signal("linchirp", n=1024)
x.dwt <- wavDWT(x, n.levels = 3)
x.modwt <- wavMODWT(x, n.levels = 3)

## calculate the wavelet details for all crystals 
## of the DWT and MODWT 
wavMRD(x.dwt)
wavMRD(x.modwt)

## plot the wavelet details for levels 1 and 3 of 
## the MODWT 
plot(wavMRD(x.modwt, level = c(1,3)))

## plot the wavelet details for all levels of the 
## MODWT of a linear chirp. 
plot(wavMRD(x.modwt))

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