wavCWTTree(x, n.octave.min=1, tolerance=0.0, type="maxima")wavCWT (as produced by the wavCWT function)."extrema", "maxima" and "minima". Default: "maxima".wavCWTTree. See DETAILS section for more information.
x[2:5]. To extract branches which terminate near times 0.47, 0.3, and 1.4, use the syntax
x[time=c(0.47, 0.3, 1.4)]. To extract all branches which terminate between times 1.2 and 1.5, use the syntax
x[range=c(1.2, 1.5)].x is an output of the wavCWTTree function):
fit=TRUE, a subset of branches (limited to four) are fit with
various linear regression models on a log(|WTMM|) versus log(scale) basis. The models are specified by the
optional models argument. This scheme illustrates the process by which
exponents are estimated using the WTMM branches. For example, to see the regressions over chains 10 through 13,
issue plot(x[10:13], fit=TRUE). Default: FALSE.fit=TRUE. Default: c("lm", "lmsreg", "ltsreg").TRUE, the branch number is placed at the head of each branch. Default: TRUE.TRUE, the locations of the (non-pruned and unbranched) extrema are
marked in the time-scale plane. Default: FALSE.par function. Default: "o".A point in the CWT $W(t,j)$ is defined
as an extremum if $|W(t-1,j)| + tol < |W(t,j)|$ and $|W(t+1,j)| + tol < |W(t,j)|$
where tol is a (scale-dependent) tolerance specified by the user.
The search algorithm is also adpated to identify plateaus in the data,
and will select the the middle of the plateau as a maximum location
when encountered. The data $|W(t,j)|$ is first scaled so that its
maximum value is 1.0, so the tolerances should be adjusted accordingly.
Since the CWT coefficients are (in effect) a result band-pass filtering operations,
the large scale coefficients form a smoother curve than do the small
scale coefficients. Thus, the tolerance vector allows the user to specify
scale-dependent tolerances, helping to weed out undesirable local maxima.
It is recommended that the tolerance be set proportional to the scale,
e.g., tolerance=C / sqrt(scale) where $C$ is a constant
$0 < C < 1$.
The user is also allowed to control the types of peaks to pursue in
the CWT plane: extrema, maxima, or minima. The algorithm (described above) is
adjusted accordingly.
The output object contains a list of sublists, each sublist corresponds to a single branch in the CWT tree and contains the named vectors:
In addition, the returned object contains the following attributes:
wavCWT, wavCWTFilters.## create linchirp series
linchirp <- make.signal("linchirp")
## calculate the CWT
W <- wavCWT(linchirp)
## form CWT tree
W.tree <- wavCWTTree(W)
## print the object
print(W.tree)
## summarize the object
summary(W.tree)
## plot thea CWT image with a tree overlay
## (R-only)
plot(W)
if (is.R()) plot(W.tree, extrema=TRUE, add=TRUE)
## plot all CWT tree branches
plot(W.tree)
## plot a subset of CWT tree branches
plot(W.tree[5:10])
## plot an illustration of the Holder exponent
## estimation process. select branches between
## times 0.2 and 0.4 (only the first four found
## will be fitted)
plot(W.tree[range=c(0.2, 0.4)], fit=TRUE)
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