inst.pulse {DecomposeR}

Computes instantaneous frequency using the Hilbert transform

Description

Calculates instantaneous frequency using the Hilbert transform (HT), normalised Hilbert transform (NHT) or the direct quadrature (DQ) methods. Normalisation is done for NHT and DQ using Huang et al., 2009 algorithm, but the empirical normalisation scheme can fail due to overshoot or undershoot of the spline. Additional research is necessary for that last feature.

Usage

inst.pulse(
  emd = NULL,
  imf = NULL,
  m = NULL,
  dt = NULL,
  ini = NULL,
  repl = 1,
  mode = NULL,
  last = FALSE,
  plot = TRUE,
  method = "HT",
  delta = NULL,
  tolerance = 8,
  relative = TRUE,
  breaks = 500,
  bins = 100,
  cut = 18,
  lines = NULL
)

Arguments

emd

an emd object

imf

a matrix of same frequency modes to calculate the frequency from. Is overridden by emd. This allows to calculate and visualise the results for single IMFs more clearly than in a population plot.

m

a matrix of the modes to calculate the frequency from. Is overridden by emd and imf.

dt

the depth or time. Is overridden by emd.

ini

an optional vector of length n of the eventual initial Intrinsic Mode Function xy would be a demodulation of, if it is a demodulation. It will be integrated to the results as mode 1.

repl

the amount of replicates in m. Is overridden by emd.

mode

the mode sequence index to give to each replicated IMFs. Is overridden by emd.

last

whether to use the last mode (trend/residue).

plot

whether to have a plot summary of the output.

method

the IF calculation method: "HT" for Hilbert transform (default), "NHT" for normalised Hilbert transform, and "DQ" for direct quadrature. The two last require normalisation, which can sometimes fail.

delta, tolerance, relative

parameters to feed to respace for interpolation

breaks, bins, cut

parameter for the plots: breaks is fed to plot_hist, bins is fed to plot_hex, and cut defines the number of color cuts for plot_hex. For better control use plot_hist and plot_hex directly.

lines

the period of lines to be added to the plots for better visualisation

Value

a list made of $dt (depth/time), $f (instantaneous frequency), $a (instantaneous amplitude),$repl (the replicate id of each point) and $mode (the mode id of each point)

References

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. https://doi.org/10.1142/S1793536909000096.

Examples

set.seed(42)

n <- 600
t <- seq_len(n)

p1 <- 30
p2 <- 240

xy <- (1 + 0.6 * sin(t*2*pi/p2)) * sin(t*2*pi/p1)  + 2 * sin(t*2*pi/p2) +
  rnorm(n, sd = 0.5) + t * 0.01

inter_dt <- round(runif(length(xy), min = 0.5, max = 1.5),1)

dt <- cumsum(inter_dt)
dec <- extricate(xy, dt, nimf = 7, repl = 10, comb = 10,
                  factor_noise = 10, sifting = 10, speak = FALSE)
## Not run: 
plot_emd(dec, dir = tempdir())
## End(Not run)

integrity(xy, dec)
parsimony(dec)

ht   <- inst.pulse(dec, lines = c(30, 240))
gzcr <- gzc(dec)

imf <- dec$m[,4]

inst.pulse(imf = imf, dt = dt, method = "DQ")