resiftModes: Consecutive Post-Processing of Ensemble Modes

In xemd: eXtended Empirical Mode Decomposition

Consecutive Post-Processing of Ensemble Modes

Description

Re-sifts a sequence of modes, typically the averaged modes of an ensemble, by extracting the first sifted component of consecutive sums and carrying each remainder to the next mode.

Usage

resiftModes(modes, sifting)

Arguments

modes	Finite numeric matrix, samples by modes, with at least two columns D_1, \ldots, D_K.
sifting	Named list of sifting controls, as in decomposeEMD; the rule "consecutive" is rejected. The chain has K - 1 extractions, so sifting$maxModes does not apply.

Details

With u_1 = D_1 + D_2, stage i extracts a_i = E_1(u_i), keeps the remainder q_i = u_i - a_i and adds the next mode, u_{i+1} = q_i + D_{i+2}. The completed chain returns K - 1 modes and the residue q_{K-1} with "chainComplete", and

\sum_{i=1}^{K-1} a_i + q_{K-1} = \sum_{j=1}^{K} D_j.

When E_1(u_i) does not exist, the chain ends with "insufficientExtrema", the modes a_1, \ldots, a_{i-1} and the residue u_i + \sum_{j > i + 1} D_j, which keeps the same sum.

Value

A list with

modes	Double matrix, samples by the extracted modes.
residue	Numeric vector, the remainder of the chain.
iterations	Integer vector, the subtractions of each extraction.
converged	Logical vector by extraction, as in decomposeEMD.
stopReason	"chainComplete" or "insufficientExtrema".

References

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.

See Also

decomposeEEMD, decomposeEMD

Examples

Time <- seq(0, 9, length.out = 1000)
Signal <- sin(pi * Time) + sin(2 * pi * Time) + sin(6 * pi * Time) +
    0.5 * Time
set.seed(628)
Noise <- t(matrix(stats::rnorm(10L * length(Signal)), nrow = 10L,
                  byrow = TRUE))
Sifting <- list(stopRule = "doubleThreshold", thresholds = c(0.05, 0.5),
                fraction = 0.05, maxSift = 2000, boundary = "reflection",
                maxModes = Inf)
# Two of the ten realizations keep the example short.
Modes <- decomposeEEMD(Signal, noise = Noise[, 1:2], amplitudeRatio = 0.2,
                       divisor = "realizations", sifting = Sifting)$modes
OUT <- resiftModes(Modes, sifting = Sifting)
c(input = ncol(Modes), output = ncol(OUT$modes))
OUT$stopReason
max(abs(rowSums(OUT$modes) + OUT$residue - rowSums(Modes)))

xemd documentation built on Nov. 9, 2026, 1:09 a.m.