cwt_wst {wavScalogram}

Continuous wavelet transform

Description

This function computes the continuous wavelet transform for some families of wavelet bases: "MORLET", "DOG", "PAUL" and "HAAR". It is a translation from the Matlab(R) function published by Torrence and Compo (Torrence & Compo, 1998).

The difference between cwt_wst and cwt from package Rwave is that cwt_wst normalizes using L^2 and cwt uses L^1.

Usage

cwt_wst(signal,
               dt = 1,
               scales = NULL,
               powerscales = TRUE,
               wname = c("MORLET", "DOG", "PAUL", "HAAR", "HAAR2"),
               wparam = NULL,
               waverad = NULL,
               border_effects = c("BE", "PER", "SYM"),
               makefigure = TRUE,
               time_values = NULL,
               energy_density = FALSE,
               figureperiod = TRUE,
               xlab = "Time",
               ylab = NULL,
               main = NULL,
               zlim = NULL)

Arguments

signal

A vector containing the signal whose wavelet transform is wanted.

dt

Numeric. The time step of the signal.

scales

A vector containing the wavelet scales at which the CWT is computed. This can be either a vector with all the scales or, following Torrence and Compo 1998, a vector of 3 elements with the minimum scale, the maximum scale and the number of suboctaves per octave (in this case, powerscales must be TRUE in order to construct power 2 scales using a base 2 logarithmic scale). If scales is NULL, they are automatically constructed.

powerscales

Logical. It must be TRUE (default) in these cases:

• If scales are power 2 scales, i.e. they use a base 2 logarithmic scale.

• If we want to construct power 2 scales automatically. In this case, scales must be NULL.

• If we want to construct power 2 scales from scales. In this case, length(scales) must be 3.

wname

A string, equal to "MORLET", "DOG", "PAUL", "HAAR" or "HAAR2". The difference between "HAAR" and "HAAR2" is that "HAAR2" is more accurate but slower.

wparam

The corresponding nondimensional parameter for the wavelet function (Morlet, DoG or Paul).

waverad

Numeric. The radius of the wavelet used in the computations for the cone of influence. If it is not specified, it is asumed to be \sqrt{2} for Morlet and DoG, 1/\sqrt{2} for Paul and 0.5 for Haar.

border_effects

String, equal to "BE", "PER" or "SYM", which indicates how to manage the border effects which arise usually when a convolution is performed on finite-length signals.

• "BE": Padding time series with zeroes.

• "PER": Using boundary wavelets (periodization of the original time series).

• "SYM": Using a symmetric catenation of the original time series.

makefigure

Logical. If TRUE (default), a figure with the wavelet power spectrum is plotted.

time_values

A numerical vector of length length(signal) containing custom time values for the figure. If NULL (default), it will be computed starting at 0.

energy_density

Logical. If TRUE (default), divide the wavelet power spectrum by the scales in the figure and so, values for different scales are comparable.

figureperiod

Logical. If TRUE (default), periods are used in the figure instead of scales.

xlab

A string giving a custom X axis label.

ylab

A string giving a custom Y axis label. If NULL (default) the Y label is either "Scale" or "Period" depending on the value of figureperiod.

main

A string giving a custom main title for the figure. If NULL (default) the main title is either "Wavelet Power Spectrum / Scales" or "Wavelet Power Spectrum" depending on the value of energy_density.

zlim

A vector of length 2 with the limits for the z-axis (the color bar).

Value

A list with the following fields:

• coefs: A matrix of size length(signal) x length(scales), containing the CWT coefficients of the signal.

• scales: The vector of scales.

• fourierfactor: A factor for converting scales into periods.

• coi_maxscale: A vector of length length(signal) containing the values of the maximum scale from which there are border effects at each time.

References

C. Torrence, G. P. Compo. A practical guide to wavelet analysis. B. Am. Meteorol. Soc. 79 (1998), 61–78.

Examples

dt <- 0.1
time <- seq(0, 50, dt)
signal <- c(sin(pi * time), sin(pi * time / 2))
cwt <- cwt_wst(signal = signal, dt = dt, energy_density = TRUE)