Description Usage Arguments Value References Examples
This function computes the normalized scalogram of a signal for the scales given. It is important to note that the notion of scalogram here is analogous to the spectrum of the Fourier transform. It gives the contribution of each scale to the total energy of the signal. For each scale s, it is defined as the square root of the integral of the squared modulus of the wavelet transform w.r.t. the time variable t, i.e.
S(s):=(integral_{∞}^{+∞}Wf(t,s)^2 dt)^{1/2}.
"Normalized" means that the scalogram is divided by the square root of the number of
times, for comparison purposes between different values of the parameter
border_effects
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  scalogram(signal,
dt = 1,
scales = NULL,
powerscales = TRUE,
wname = c("MORLET", "DOG", "PAUL", "HAAR", "HAAR2"),
wparam = NULL,
waverad = NULL,
border_effects = c("BE", "INNER", "PER", "SYM"),
energy_density = TRUE,
makefigure = TRUE,
figureperiod = TRUE,
xlab = NULL,
ylab = "Scalogram",
main = "Scalogram")

signal 
A vector containing the signal whose scalogram is wanted. 
dt 
Numeric. The time step of the signal. 
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 
Logical. It must be TRUE (default) in these cases:

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 √{2} for Morlet and DoG, 1/√{2} for Paul and 0.5 for Haar. 
border_effects 
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 finitelenght signals.

energy_density 
Logical. If TRUE (default), divide the scalogram by the square root of the scales for convert it into energy density. 
makefigure 
Logical. If TRUE (default), a figure with the scalogram is plotted. 
figureperiod 
Logical. If TRUE (default), periods are used in the figure instead of scales. 
xlab 
A string giving a custom X axis label. If NULL (default) the X label is
either "Scale" or "Period" depending on the value of 
ylab 
A string giving a custom Y axis label. 
main 
A string giving a custom main title for the figure. 
A list with the following fields:
scalog
: A vector of length length(scales)
, containing the values of
the scalogram at each scale.
scales
: The vector of scales.
energy
: If energy_density
is TRUE, it is the L^2 norm of
scalog
.
fourierfactor
: A factor for converting scales into periods.
C. Torrence, G. P. Compo. A practical guide to wavelet analysis. B. Am. Meteorol. Soc. 79 (1998), 61–78.
V. J. Bolós, R. Benítez, R. Ferrer, R. Jammazi. The windowed scalogram difference: a novel wavelet tool for comparing time series. Appl. Math. Comput., 312 (2017), 4965.
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