wavCWTPeaks(x, snr.min=3, scale.range=NULL, length.min=10, noise.span=NULL, noise.fun="quantile", noise.min=NULL)wavCWTTree.scale.range needed in order for that branches peak to be considered a peak candidate.
Default: 10.
where x is a vector of smallest-scale CWT coefficients whose time indices are near that of the branch termination time.
Default: "quantile".
quantile(attr(x,"noise"), prob=0.05),
where x is the input wavCWTTree object.NULL,max(0.01 * diff(range(times)), 5*sampling.interval),
where times and sampling.interval are attributes of the input wavCWTTree object.scale[range(which(branch.hist > quantile(branch.hist,prob=0.8)))], where branch.hist is an
attribute of the input wavCWTTree object. This default results in isolating the bulk of energetic CWT branches, but
the user in encouraged to reduce the scale range in order to attenuate the computational burden of the peak detection scheme.3.x and y vectors identifying the peaks in the original time series.
The pruning criteria (snr.min, scale.range, length.min, noise.span, noise.fun, noise.min)
are attached are attached as attributes. In addition, a peaks attribute is
attached and corresponds to a data.frame containing the following information for each peak:The local maxima of the CWT are linked together
to form so-called branches, where each branch represents one ridge of the
CWT time-scale terrain. The collection of branches forms a tree, as output
by the wavCWTTree function. The wavCWTpeaks function prunes the branches of the
input CWT tree and records the termination time (i.e., the time associated with
point of the branch that is closest to scale zero) as the time index associated
with the local peak of the corresponding time series. Information regarding the collection of isolated peaks
is returned as a data.frame object.
The tree branches are pruned in the following ways:
snr.min.
A peak SNR estimate is formed as follows:
For each branch of the input CWT tree, a subset of
CWT coefficients is collected such that the CWT coefficients are both local to the branch termination time and correspond
to the smallest analyzed CWT scale. The user specified noise.span argument is used to define the boundaries of
each subset in time ala $[B - $noise.span, $B + $noise.span$]$, where $B$ is the branch termination
time. Each CWT subset is assumed to be representative of the local noise levels near the corresponding branch termination time
and noise.fun is used to quantify (and summarize) each level resulting in a scalar $z$. The minimum value of $z$ is
specified by the user ala the noise.min argument. Finally, the ratio $|P|/|W|$ is used to form an estimate of
the local signal-to-noise ration (SNR) for the corresponding branch, where $P$ is the maximum CWT value along the
branch in the CWT time-scale plane.
scale.range.
scale.range is greater than or equal to the specified minimum length.min.
noise.span or $3$, whichever is greater.NOTE: For peak detection, the wavelet filters used to form the CWT must maintain an (approximate) zero phase
property so that the CWT coefficients can be meaningfully aligned with the events of the original
time series. Currently, only the so-called Mexican hat wavelet maintains this property due to
the even-symmetry of the filter's impulse response. Therefore, only the Mexican hat wavelet ("gaussian2")
is currently supported for CWT-based peak detection. See the wavCWTFilters and wavCWT
function for more information.
J.F. Muzy, E. Bacry, and A. Arneodo., ``The multifractal formalism revisited with wavelets.", International Journal of Bifurcation and Chaos, 4, 245--302 (1994).
wavCWTTree, wavCWT, wavCWTFilters.## create linchirp series
linchirp <- make.signal("linchirp")
## calculate the CWT
W <- wavCWT(linchirp)
## form CWT tree
z <- wavCWTTree(W)
## estimate the peak locations using default
## scale.range
p <- wavCWTPeaks(z)
## plot an overlay of the original series and the
## peaks
x <- as(linchirp@positions,"numeric")
y <- linchirp@data
plot(x, y, type="l", xlab="time", ylab="linchirp")
points(p, pch=16, col="red", cex=1.2)
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