normalise {DecomposeR}

Empirical AM and FM decomposition

Description

Applies the normalisation scheme of Huang et al., 2009 to decompose any Intrinsic Mode Functions obtained (usually via Empirical Mode Decomposition) into an Frequency Modulated component of amplitude 1, also called carrier, and its Amplitude Modulated enveloppe. The carrier can then be used to compute the instantaneous frequency via the Normalised Hilbert Transform (NHT) or by calculating its Direct Quadrature (DQ) (Huang et al., 2009). HOWEVER THIS FUNCTION CAN FAIL due to overshoot or undershoot of the spline fitting. Additional research is necessary.

Usage

normalise(emd = NULL, m = NULL, dt = NULL, repl = 1, last = TRUE, speak = TRUE)

normalize(emd = NULL, m = NULL, dt = NULL, repl = 1, last = TRUE, speak = TRUE)

Arguments

emd

an emd object

m

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

dt

the depth or time. Is overridden by emd.

repl

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

last

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

speak

whether to print a sentence at each iteration

Value

a list of two matrices: $fc (frequency carrier) and $a (instantaneous 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

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)

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

dt <- cumsum(inter_dt)

dec <- extricate(xy, dt, nimf = 7, sifting = 10,
               repl = 1, comb = 100, factor_noise = 10,
               speak = TRUE)

plot_emd(dec, pdf = FALSE, select = 4)

integrity(xy, dec)
parsimony(dec)

m  <- dec$m

res <- normalise(dt = dt, m = m, last = FALSE)

numb <- 4

opar <- par('mfrow')

par(mfrow = c(1,2))

plot(m[,numb], dt, type = "l", xlab = "xy",
     main = paste("Mode", numb, "and AM enveloppe"))
lines(res$a[,numb], dt, col = "red", lty = 5, lwd = 2)

plot(res$fc[,numb], dt, type = "l", xlab = "xy",
     main = "FM carrier")

par(mfrow = opar)