Noise-Assisted Multivariate Empirical Mode Decomposition

Decomposes a signal together with supplied noise channels by one multivariate decomposition and keeps the coordinates of the signal.

Usage

decomposeNAMEMD(signal, noiseChannels, directionCount = 64, sifting)

Arguments

signal: Numeric matrix of finite real values, samples by channels, with one or more columns.
noiseChannels: Numeric matrix of finite real values with the rows of signal and \(Q \ge 1\) columns, in the units of the signal, supplied by the caller: the function draws no random numbers. emdr draws its noise with standard deviation 0.02 on standardized channels.
directionCount: Whole number of Hammersley points, as in decomposeMEMD; default 64.
sifting: Named list of sifting controls, as in decomposeMEMD.

Details

The function runs decomposeMEMD on the augmented matrix \(\mathbf{y} = [\mathbf{x}, \mathbf{w}]\) and keeps the first \(C\) coordinates of every mode, \(\mathbf{c}_k = P_x \tilde{\mathbf{c}}_k\), and of the residue. Projections, stopping, iterations and termination are those of the augmented decomposition. In decomposeTSL the noise channels are drawn by group with noiseChannelCount and scaled by noiseRatio times the reference deviation of the group.

Value

A list with the fields of decomposeMEMD; modes has the \(C\) channels of signal and residue its \(C\) columns.

References

ur Rehman, N. and Mandic, D. P. (2011). Filter Bank Property of Multivariate Empirical Mode Decomposition. IEEE Transactions on Signal Processing, 59(5), 2421–2426. doi:10.1109/TSP.2011.2106779

The selection of the reflected extrema and the spline interpolation of the envelope nodes are adapted from emd.m (G. Rilling, March 2007), distributed with CEEMDAN revision af9a0f83, copyright (c) 2020 Marcelo A. Colominas, MIT License; see the NOTICE file of the installed package.

Examples

Time <- 2 * pi * (0:511) / 512
z <- cos(0.3 * Time) * exp(2i * Time) +
    0.3 * abs(sin(2.3 * Time)) * exp(17i * Time)
Signal <- cbind(Re(z), Im(z))
set.seed(628)
# Two noise channels with 0.02 times the reference deviation of the signal.
Noise <- 0.02 * sqrt(mean(apply(Signal, 2, stats::sd)^2)) *
    matrix(stats::rnorm(512 * 2), nrow = 512)
OUT <- decomposeNAMEMD(Signal, noiseChannels = Noise, directionCount = 64,
                       sifting = list(stopRule = "fixed", fixedSift = 1,
                                      boundary = "reflection",
                                      maxModes = 3))
dim(OUT$modes)
#> [1] 512   3   2
dim(OUT$residue)
#> [1] 512   2