WaverideR (version 0.4.1)

analyze_wavelet: Conduct the continuous wavelet transform on a time series/signal

Description

Compute the continuous wavelet transform (CWT) using a Morlet wavelet

Usage

analyze_wavelet(
  data = NULL,
  dj = 1/100,
  lowerPeriod = 2,
  upperPeriod = 1024,
  verbose = FALSE,
  omega_nr = 8,
  pval = FALSE,
  n_simulations = 10,
  run_multicore = FALSE
)

Value

The output is a list (wavelet object) which contain 20 objects which are the result of the continuous wavelet transform (CWT). Object 1: Wave - Wave values of the wavelet Object 2: Phase - Phase of the wavelet Object 3: Ampl - Amplitude values of the wavelet Object 4: Power - Power values of the wavelet Object 5: dt - Step size Object 6: dj - Scale size Object 7: Power.avg - Average power values Object 8: Period - Period values Object 9: Scale - Scale value Object 10: coi.1 - Cone of influence values 1 Object 11: coi.2 - Cone of influence values 2 Object 12: nc - Number of columns Object 13: nr - Number of rows Object 14: axis.1 - axis values 1 Object 15: axis.2 - axis values 2 Object 16: omega_nr - Number of cycles in the wavelet Object 17: x - x values of the data set Object 18: y - y values of the data set Object 19: average p value of the spectral power Object 20: p value of spectral power

Arguments

data

Input data, should be a matrix or data frame in which the first column is depth or time and the second column is proxy record.

dj

Spacing between successive scales. The CWT analyses analyses the signal using successive periods which increase by the power of 2 (e.g.2^0=1,2^1=2,2^2=4,2^3=8,2^4=16). To have more resolution in-between these steps the dj parameter exists, the dj parameter specifies how many extra steps/spacing in-between the power of 2 scaled CWT is added. The amount of steps is 1/x with a higher x indicating a smaller spacing. Increasing the increases the computational time of the CWT Default=1/200.

lowerPeriod

Lowest period to be analyzed Default=2. The CWT analyses the signal starting from the lowerPeriod to the upperPeriod so the proper selection these parameters allows to analyze the signal for a specific range of cycles. scaling is done using power 2 so for the best plotting results select a value to the power or 2.

upperPeriod

Upper period to be analyzed Default=1024. The CWT analyses the signal starting from the lowerPeriod to the upperPeriod so the proper selection these parameters allows to analyze the signal for a specific range of cycles. scaling is done using power 2 so for the best plotting results select a value to the power or 2.

verbose

Print text Default=FALSE.

omega_nr

Number of cycles contained within the Morlet wavelet

pval

calculate the P-value Default=FALSE. The p-value is based on Monte Carlo modelling runs on surrogate data generated based on autocorrelated noise (red noise) the calculated using a windowed (the window is half the size of the data set) temporal autocorrelation and on shuffling the data set resulting in a random data sets which has similar spectral characteristics to the original data set.The shuffling of the data set creates white noise which ensures that high amplitude high frequency/short period cycles do not result in statistical significant peaks. The part of the data generated using the autocorrelated noise (red noise) based on the windowed (the window is half the size of the data set) temporal autocorrelation represent a spectral signature similar to to that of the original data. The original data might include spectral peaks which are the result of astronomical forcing. The result is that the spectral power profile is biased towards rejecting the 0-hypothesis (e.g. no astronomical forcing). By combining the shuffling of the data set with autocorrelated noise a surrogate data set is created which rejects high amplitude high frequency/short period cycles and a reduced biased towards towards rejecting the 0-hypothesis if the data was solely the result of autocorrelated noise

n_simulations

Number of simulation to be ran to generate the p-value

run_multicore

Run p-value calculation with one core or multiple cores

Author

Code based on on the "WaveletComp" function of the 'WaveletComp' R package and "wt" function of the 'biwavelet' R package which are based on the wavelet MATLAB code written by Christopher Torrence and Gibert P. Compo.

References

Angi Roesch and Harald Schmidbauer (2018). WaveletComp: Computational Wavelet Analysis. R package version 1.1. https://CRAN.R-project.org/package=WaveletComp

Gouhier TC, Grinsted A, Simko V (2021). R package biwavelet: Conduct Univariate and Bivariate Wavelet Analyses. (Version 0.20.21), https://github.com/tgouhier/biwavelet

Torrence, C., and G. P. Compo. 1998. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:61-78. https://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf

Morlet, Jean, Georges Arens, Eliane Fourgeau, and Dominique Glard. "Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media. " Geophysics 47, no. 2 (1982): 203-221.

J. Morlet, G. Arens, E. Fourgeau, D. Giard; Wave propagation and sampling theory; Part II, Sampling theory and complex waves. Geophysics 1982 47 (2): 222–236.

Examples

# \donttest{
#Example 1. Using the Total Solar Irradiance data set of Steinhilver et al., (2012)
TSI_wt <-
 analyze_wavelet(
   data = TSI,
   dj = 1/200,
   lowerPeriod = 16,
   upperPeriod = 8192,
   verbose = FALSE,
   omega_nr = 6,
   pval=FALSE,
   n_simulations=10,
   run_multicore = FALSE
 )


#Example 2. Using the magnetic susceptibility data set of Pas et al., (2018)
mag_wt <-
analyze_wavelet(
data = mag,
dj = 1/100,
lowerPeriod = 0.1,
upperPeriod = 254,
verbose = FALSE,
omega_nr = 10,
pval=FALSE,
n_simulations=10,
run_multicore = FALSE
)

#Example 3. Using the greyscale data set of Zeeden et al., (2013)
grey_wt <-
 analyze_wavelet(
   data = grey,
   dj = 1/200,
   lowerPeriod = 0.02,
   upperPeriod = 256,
   verbose = FALSE,
   omega_nr = 8,
   pval=FALSE,
   n_simulations=10,
   run_multicore = FALSE
 )

# }