gzc.algorithm {DecomposeR}

Calculates instantaneous frequency of simplified IMF using the GZC method

Description

Calculates instantaneous frequency of simplified IMF using the Generalised Zero-Crossing method from Huang et al., 2009.

Usage

gzc.algorithm(xy, dt)

Arguments

xy

a matrix of amplitude

dt

a vector of depth or time values

Details

the GZC method is precise to 1/4th of a period, so the results are provided between left and right points, i.e. either an extrema or a zero-crossing.

Value

a list of $ldt (left position), $rdt (right position), $f (frequency) and $a (amplitude)

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

xyi  <- c(0.5,0,-0.5,0,0.5,0,-0.5,0,0.5,0,-0.5,0,0.5,0,-0.5,0,0.5,0,-0.5,0,
         1,1,0,-1,-1,0,1,1,0,-1,-1,0,1,1,0,-1,-1)

dti <- 1:length(xyi)

d <- simp.emd(m = xyi, dt = dti)

xy <- d$xy
dt <- d$dt

res <- gzc.algorithm(xy, dt)

opar <- par('mfrow')

par(mfrow = c(2,1))

plot(dti, xyi, pch = 19, type = "o", ylab = "xy", xlab = "dt")
points(dt, xy, pch = 19, col = "green")
points(res$ldt, res$a, pch = 19, col = "red")
points(res$rdt, res$a, pch = 19, col = "red")

plot(dt, rep(max(res$f, na.rm = TRUE), length(dt)), type = "n",
     ylab = "Frequency", xlab = "dt",
     ylim = c(0, 2 * max(res$f, na.rm = TRUE)))
points(res$ldt, res$f, pch = 19)
points(res$rdt, res$f, pch = 19)

par(mfrow = opar)