scale_index {wavScalogram}

Scale index of a signal

Description

This function computes the scale index of a signal in the scale interval [s_0,s_1], for a given set of scale parameters s_1 and taking s_0 as the minimum scale (see Benítez et al. 2010).

The scale index of a signal in the scale interval [s_0,s_1] is given by the quotient

\frac{S(s_{min})}{S(s_{max})},

where S is the scalogram, s_{max} \in [s_0,s_1] is the smallest scale such that S(s)\le S(s_{max}) for all s \in [s_0,s_1], and s_{min} \in [s_{max},2s_1] is the smallest scale such that S(s_{min})\le S(s) for all s \in [s_{max},2s_1].

Usage

scale_index(signal = NULL,
                   scalog = NULL,
                   dt = 1,
                   scales = NULL,
                   powerscales = TRUE,
                   s1 = NULL,
                   wname = c("MORLET", "DOG", "PAUL", "HAAR", "HAAR2"),
                   wparam = NULL,
                   waverad = NULL,
                   border_effects = c("BE", "INNER", "PER", "SYM"),
                   makefigure = TRUE,
                   figureperiod = TRUE,
                   plot_scalog = FALSE,
                   xlab = NULL,
                   ylab = "Scale index",
                   main = "Scale Index")

Arguments

signal

A vector containing the signal whose scale indices are wanted.

scalog

A vector containing the scalogram from which the scale indices are going to be computed. If scalog is not NULL, then signal, waverad and border_effects are not necessary and they are ignored.

dt

Numeric. The time step of the signals.

scales

A vector containing the wavelet scales at wich the scalogram 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.

s1

A vector containing the scales s_1. The scale indices are computed in the intervals [s_0,s_1], where s_0 is the minimum scale in scales. If s1 are not power 2 scales, then scales should not be power 2 scales either and hence, powerscales must be FALSE.

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

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

• "BE": With border effects, padding time series with zeroes.

• "INNER": Normalized inner scalogram with security margin adapted for each different scale.

• "PER": With border effects, using boundary wavelets (periodization of the original time series).

• "SYM": With border effects, using a symmetric catenation of the original time series.

makefigure

Logical. If TRUE (default), a figure with the scale indices is plotted.

figureperiod

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

plot_scalog

Logical. If TRUE, it plots the scalogram from which the scale indices are computed.

xlab

A string giving a custom X axis label. If NULL (default) the X label is either "s1" or "Period of s1" depending on the value of figureperiod.

ylab

A string giving a custom Y axis label.

main

A string giving a custom main title for the figure.

Value

A list with the following fields:

• si: A vector with the scale indices.

• s0: The scale s_0.

• s1: A vector with the scales s_1.

• smax: A vector with the scales s_{max}.

• smin: A vector with the scales s_{min}.

• scalog: A vector with the scalogram from which the scale indices are computed.

• scalog_smax: A vector with the maximum scalogram values S(s_{max}).

• scalog_smin: A vector with the minimum scalogram values S(s_{min}).

• fourierfactor: A factor for converting scales into periods.

References

R. Benítez, V. J. Bolós, M. E. Ramírez. A wavelet-based tool for studying non-periodicity. Comput. Math. Appl. 60 (2010), no. 3, 634-641.

Examples

dt <- 0.1
time <- seq(0, 50, dt)
signal <- c(sin(pi * time), sin(pi * time / 2))
si <- scale_index(signal = signal, dt = dt)

# Another way, giving the scalogram instead of the signal:

sc <- scalogram(signal = signal, dt = dt, energy_density = FALSE, makefigure = FALSE)
si <- scale_index(scalog = sc$scalog, scales = sc$scales, dt = dt)