plot.wd

Plot wavelet transform coefficients.

DESCRIPTION

USAGE

plot.wd(wd, xlabvals, first.level = 0,
	main = "Wavelet Decomposition Coefficients", scaling = "global",
	rhlab = F, sub, NotPlotVal = 0.005, xlab = "Translate",
	ylab = "Resolution Level", 
	aspect = "Identity", ...)

REQUIRED ARGUMENTS

wd

The wd object whose coefficients you wish to plot.

OPTIONAL ARGUMENTS

xlabvals

A vector containing the "true" x-axis numbers that went with the vector that was transformed to produce the wd object supplied as the first argument to this function. If this argument is missing then the function tries to make up a sensible set of x-axis labels.

first.level

The first resolution level to begin plotting at. This argument can be quite useful when you want to supress some of the coarser levels in the diagram.

main

The main title of the plot.

scaling

How you want the coefficients to be scaled. The options are: global - one scale factor is chosen for the whole plot. The scale factor depends on the coefficient to be included on the plot that has the largest absolute value. The global option is useful when comparing coefficients that might appear anywhere in the plot; by.level - a scale factor is chosen for each resolution level in the plot. The scale factor for a level depends on the coefficient in that level that has the largest absolute value. The by.level option is useful when you wish to compare coefficients within a resolution level.

The two other options are compensated and super which are the same as global except for that finer scales' coefficients are scaled up by a factor of SQRT(2) for compensated and 2 for super. These latter two options are sometimes useful (more useful for non-decimated wd objects, where they act as a sort of ipndacw matrix operator).

rhlab

If T then a set of labels is produced on the right hand axis. The axis labels in this case refer to the scale factors used to scale each level and correspond to value of the largest coefficient (in absolute value) in each scale (when scaling=="by.level") or absolutely (when scaling="global"). If the rhlab argument is F then no right hand axis labels are produced.

sub

A subtitle for the plot.

NotPlotVal

This argument ensures that if all (scaled) coefficients in a resolution level are below NotPlotVal in absolute value then the whole resolution level is not plotted. This can be useful when plotting a wd object that is sparse (or has been thresholded and necessarily many coefficients might well be zero) as it speeds up the plot because whole levels do not have to be plotted (the function that does the plotting [segments()] is quite a slow function). Note that the value of NotPlotVal refers to scaled coefficients, those that have been scaled by this function (on any resolution level all coefficients are scaled to lie between -0.5 and 0.5).

xlab

A title for the x-axis

ylab

A title for the y-axis

aspect

This argument describes the name (as a character string) of a function to be applied to the coefficients before plotting. By default the argument is "Identity", i.e. the coefficients are plotted as is. This argument is most useful when a complex-valued wavelets are plotted you could use "Mod" to plot the modulus of the coefficients, or "Re" to plot the real parts of the coefficients or "Arg" to plot the argument of the coefficients. Also, the aspect argument can be useful for the ordinary wavelet transforms as well if you are interested in a particular transform of the coefficients.

VALUE

SIDE EFFECTS

DETAILS

A wavelet decomposition of a signal consists of discrete wavelet coefficients at different scales (resolution levels) and locations. This function plots the coefficients as a pyramid (derived from Mallat's pyramid algorithm). See the examples below.

The resolution levels are stacked one above the other: coarse scale coefficients are always towards the top of the plot, fine scale coefficients are always located toward the bottom of the plot. The location of coefficients increases from left to right across the plot in synchrony with the input signal to the wd object. In other words the position of a coefficient along a line is indicative of the associated wavelet basis function's translate number. The actual coefficients are plotted using S-Plus's segments() function. This plots each coefficient as a vertical line with positive coefficients being plotted above an imaginary centre line and negative coefficients being plotted below.

The resolution levels are labelled on the left-hand side axis, and if rhlab==T the maximum values of the absolute values of the coefficients, for the particular level, are plotted on the right-hand axis.

The coefficients in the plot may be scaled in 4 ways. If you are interested in comparing coefficients in different levels then the default scaling option scaling=="global" is what you need. This works by finding the coefficient with the largest absolute value amongst all coeffients to be plotted and then scales all the other coefficients by the largest so that all coefficients lie in the range -1/2 to 1/2. The scaled coefficients are then plotted. If you are not interested in comparing relative resolution levels and want to see all that goes on within a particular scale then you should use the scaling option scaling=="by.level" which picks out the largest coefficient (in absolute value) from each level and scales each level separately. The "compensated" and super options are like the "global" option except that finer levels are scaled up (as discussed in the arguments list above): this can be useful when plotting non-decimated wavelet transform coefficients as it emphasizes the higher frequencies.

RELEASE

SEE ALSO

EXAMPLES

#
# Generate some test data
#
> test.data <- example.1()$y
> tsplot(test.data)

#
# Decompose test.data and plot the wavelet coefficients
#
> wds <- wd(test.data)
> plot(wds)

#
# Now do the time-ordered non-decimated wavelet transform of the same thing
#
> wdS <- wd(test.data, type="station")
> plot(wdS)

#
# Next example
# ------------
# The chirp signal is also another good example to use.
#
# Generate some test data
#
> test.chirp <- simchirp()$y
> tsplot(test.chirp, main="Simulated chirp signal")

#
# Now let's do the time-ordered non-decimated wavelet transform.
# For a change let's use Daubechies least-asymmetric phase wavelet with 8
# vanishing moments (a totally arbitrary choice, please don't read
# anything into it).
#
> chirpwdS <- wd(test.chirp, filter.number=8, family="DaubLeAsymm", type="station")
> plot(chirpwdS, main="TOND WT of Chirp signal")