Extract signal from a wavelet spectra using a traced period curve

Extract signal power from the wavelet in the depth domain using the traced period.

Usage

extract_signal(
  tracked_cycle_curve = NULL,
  wavelet = NULL,
  period_up = 1.2,
  period_down = 0.8,
  add_mean = TRUE,
  tracked_cycle_period = NULL,
  extract_cycle = NULL,
  tune = FALSE,
  plot_residual = FALSE
)

Arguments

tracked_cycle_curve: Tracked period of the cycle along the record (matrix or data frame: depth/time in column 1, period in column 2, in the depth/time unit of the wavelet), e.g. the output of track_period_wavelet completed with completed_series, optionally smoothed with loess_auto. Rows with NA are dropped and the curve is linearly interpolated (and extrapolated) to the depth/time axis of the wavelet. Required (Default=NULL).
wavelet: Wavelet object (list) created with analyse_wavelet; the signal is reconstructed from its coefficients. Required (Default=NULL).
period_up: Upper boundary of the band that is reconstructed, as a factor of the (rescaled) tracked period (numeric, > period_down). Default=1.2.
period_down: Lower boundary of the band that is reconstructed, as a factor of the (rescaled) tracked period (numeric, > 0). Default=0.8.
add_mean: Add the mean of the original data series to the extracted cycle (logical, TRUE or FALSE); FALSE returns it centred on zero. Default=TRUE.
tracked_cycle_period: Duration in time of the tracked cycle, e.g. 405 (kyr) for the long eccentricity cycle (numeric, > 0), in the same unit as extract_cycle. The tracked curve is multiplied by extract_cycle / tracked_cycle_period; also used for the tuning when tune=TRUE. Required (Default=NULL).
extract_cycle: Duration of the cycle to extract (numeric, > 0), in the same unit as tracked_cycle_period; use the same value to extract the tracked cycle itself. Required (Default=NULL).
tune: Convert the extracted cycle from the depth to the time domain with curve2tune, using tracked_cycle_curve and tracked_cycle_period (logical, TRUE or FALSE). Default=FALSE.
plot_residual: Plot the residual (extracted cycle minus data) against depth and its histogram (logical, TRUE or FALSE). Default=FALSE.

Value

Returns a matrix with 2 columns The first column is depth/time The second column is extracted signal

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

Author

Code based on the reconstruct function of the 'WaveletComp' R package which is based on the wavelet 'MATLAB' code written by Christopher Torrence and Gibert P. Compo (1998).

Examples

# \donttest{
#Extract the 405 kyr eccentricity cycle from the the magnetic susceptibility \cr
#record of the Sullivan core and use the Gabor uncertainty principle to define \cr
#the mathematical uncertainty of the analysis and use a factor of that standard \cr
#deviation to define boundaries.

#Perform the CWT
mag_wt <- analyse_wavelet(data = mag,
dj = 1/100,
lowerPeriod = 0.1,
upperPeriod = 254,
verbose = FALSE,
omega_nr = 10)

#Track the 405 kyr eccentricity cycle in a wavelet spectra

#mag_track <- track_period_wavelet(astro_cycle = 405,
#                                   wavelet=mag_wt,
#                                   n.levels = 100,
#                                   periodlab = "Period (metres)",
#                                   x_lab = "depth (metres)")

#Instead of tracking, the tracked solution data set \code{\link{mag_track_solution}} is used \cr
mag_track <- mag_track_solution


mag_track_complete <- completed_series(
  wavelet = mag_wt,
  tracked_curve = mag_track,
  period_up = 1.2,
  period_down = 0.8,
  extrapolate = TRUE,
  genplot = FALSE
)

# smooth the tracking of the 405 kyr eccentricity cycle
mag_track_complete <- loess_auto(time_series = mag_track_complete,
genplot = FALSE, print_span = FALSE)

# extract the 405 kyr eccentricity cycle from the wavelet spectrum and use the \cr
# tracked cycle curve and set factors of the extracted cycle as boundaries

mag_405_ecc  <- extract_signal(
tracked_cycle_curve = mag_track_complete,
wavelet = mag_wt,
period_up = 1.2,
period_down = 0.8,
add_mean = TRUE,
tracked_cycle_period = 405,
extract_cycle = 405,
tune = FALSE,
plot_residual = FALSE
)
# }