Multitaper synchrosqueezing (ConceFT) of a record — analyse

Computes the "Concentration of Frequency and Time" (ConceFT) representation of Daubechies, Wang and Wu (2016), a multitaper version of the wavelet synchrosqueezing transform that is robust against noise. The synchrosqueezed transform of a noisy record contains spurious short ridges because noise also has an instantaneous frequency. ConceFT uses a set of K orthonormal generalised Morse wavelets (Olhede and Walden 2002) and computes the synchrosqueezed transform for many random linear combinations of them (random unit vectors). The noise in these transforms is (nearly) independent while the ridges of the cycles are the same, so the average keeps the cycles and averages the noise away, with much less broadening than averaging the scalograms of the separate wavelets (method = "multitaper", which is also available).

Usage

analyse_conceft(
  data = NULL,
  lowerPeriod = 2,
  upperPeriod = 1024,
  dj = 1/100,
  gamma = 3,
  beta = 20,
  K = 2,
  n_comb = 20,
  method = c("conceft", "multitaper"),
  sst_order = 1,
  n_iter = 1,
  threshold = "riskshrink",
  seed = 1,
  verbose = FALSE
)

analyze_conceft(
  data = NULL,
  lowerPeriod = 2,
  upperPeriod = 1024,
  dj = 1/100,
  gamma = 3,
  beta = 20,
  K = 2,
  n_comb = 20,
  method = c("conceft", "multitaper"),
  sst_order = 1,
  n_iter = 1,
  threshold = "riskshrink",
  seed = 1,
  verbose = FALSE
)

Arguments

data: Input record: a matrix or data frame with depth/time in column 1 and the proxy value in column 2 (further columns are ignored). Incomplete rows are removed, the rows are sorted by depth/time, the record is linearly interpolated to the median sampling interval and standardised. Required (Default=NULL gives an error).
lowerPeriod, upperPeriod: Shortest and longest period of the transform, in the same unit as the depth/time column of data (numeric, 0 < lowerPeriod < upperPeriod; lowerPeriod at least twice the sampling interval). Defaults: lowerPeriod: Default=2; upperPeriod: Default=1024.
dj: Spacing of the period axis in octaves (numeric, > 0; 1/x gives x periods per doubling of the period). Default=1/100.
gamma, beta: Parameters gamma and beta of the generalised Morse wavelets (numeric, > 0); the defaults are Lilly's default family (Daubechies et al. 2016 used gamma = 9, beta = 30). A larger beta gives longer wavelets (better period resolution, worse depth/time resolution). Defaults: gamma: Default=3; beta: Default=20.
K: Number of orthonormal Morse wavelets (tapers) of orders 0 to K-1 (integer, >= 1). More tapers suppress noise better but broaden the ridges. Default=2.
n_comb: Number of random combinations of the tapers whose synchrosqueezed transforms are averaged (integer, >= 1); only used when method="conceft". The first combination is always the zero-order Morse wavelet itself. More combinations average out more noise at a higher computation time. Default=20.
method: Averaging method (character), one of "conceft" (average over n_comb random unit-vector combinations of the K tapers) or "multitaper" (average of the synchrosqueezed transforms of the K orthonormal wavelets themselves). Default="conceft" (the first element of c("conceft", "multitaper")).
sst_order: Order of the synchrosqueezing of every combination (numeric, 1 or 2), see analyse_wavelet_sst. Default=1.
n_iter: Number of iterations of the frequency reassignment of every combination (integer, >= 1), see analyse_wavelet_sst. Default=1.
threshold: Noise threshold of the synchrosqueezing: "riskshrink", "none" or a number (numeric, in standard deviations of the standardised record), see analyse_wavelet_sst. Default="riskshrink".
seed: Seed of the random number generator used to draw the random combinations (integer), so that results are reproducible; the previous random state is restored afterwards. Only used when method="conceft". Default=1.
verbose: Print a message after each combination (logical, TRUE or FALSE). Default=FALSE.

Value

A list of class analyze.wavelet (see analyse_wavelet_sst) with the averaged power in Power; Wave has this power with the phase of the synchrosqueezed transform of the first (zero order) Morse wavelet, so the extraction functions can use it.

References

Daubechies, I., Wang, Y., Wu, H.-T., 2016. ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform. Philosophical Transactions of the Royal Society A 374, 20150193.

Olhede, S.C., Walden, A.T., 2002. Generalized Morse wavelets. IEEE Transactions on Signal Processing 50, 2661-2670.

Lilly, J.M., Olhede, S.C., 2012. Generalized Morse wavelets as a superfamily of analytic wavelets. IEEE Transactions on Signal Processing 60, 6036-6041.

Examples

# \donttest{
z <- 0:999
x <- sin(2 * pi * z / 40) + sin(2 * pi * z / 50) + rnorm(length(z), sd = 1.5)
cf <- analyse_conceft(data.frame(z, x), lowerPeriod = 20, upperPeriod = 100, dj = 1 / 50,
    n_comb = 10)
plot_wavelet(cf)

# }