WaverideR (version 0.4.1)

Hilbert_transform: Perform a Hilbert transform on a signal

Description

Extract the amplitude modulation using the Hilbert transform.

Usage

Hilbert_transform(data = NULL, demean = TRUE, nr_pad = 100)

Value

Returns a matrix with 2 columns. The first column is depth/time. The second column is the Hilbert transform of the signal.

Arguments

data

Input is a time series with the first column being depth or time and the second column being a proxy.

demean

Remove the mean from the time series.

nr_pad

nr of points added tot the top and bottom of the data set to mitigate the edging effect of the Hilbert transform.

Author

Based on the the inst.pulse function of the 'DecomposeR' R package.

References

Wouters, S., Crucifix, M., Sinnesael, M., Da Silva, A.C., Zeeden, C., Zivanovic, M., Boulvain, F., Devleeschouwer, X., 2022, "A decomposition approach to cyclostratigraphic signal processing". Earth-Science Reviews 225 (103894). <doi:10.1016/j.earscirev.2021.103894>

Huang, Norden E., Zhaohua Wu, Steven R. Long, Kenneth C. Arnold, Xianyao Chen, and Karin Blank. 2009. "On Instantaneous Frequency". Advances in Adaptive Data Analysis 01 (02): 177–229. <doi:10.1142/S1793536909000096>

Examples

#Example in which the Hilbert transform (eg. amplitude modulation) of the ~210yr
#de Vries cycle is extracted from the Total Solar Irradiance data set of
#Steinhilber et al., (2012)

#Perform the CWT
TSI_wt <-
analyze_wavelet(
data = TSI,
dj = 1/200,
lowerPeriod = 16,
upperPeriod = 8192,
   verbose = FALSE,
   omega_nr = 6
 )

#Extract the 210 yr de Vries cycle from the wavelet spectra
de_Vries_cycle <- extract_signal_stable(wavelet=TSI_wt,
cycle=210,
period_up =1.25,
period_down = 0.75,
add_mean=TRUE,
plot_residual=FALSE)

#Perform the Hilbert transform on the amplitude record of the 210 yr de Vries
# cycle which was extracted from the wavelet spectra

de_Vries_cycle_hilbert <- Hilbert_transform(data=de_Vries_cycle,demean=TRUE)