xemd

xemd provides R functions for signal decomposition and mode analysis. The library and the xemd command-line interface are installed together from the repository root with the product installer.

In empirical mode decomposition (EMD), the signal’s extrema define the local scales used to extract components. Each extracted component is subtracted from the remaining signal, leaving a final residue. Hilbert analysis describes each component through its analytic signal: its modulus gives instantaneous amplitude, and the derivative of its continuous phase divided by 2\pi gives instantaneous frequency where that phase is defined and differentiable. The introduction develops these concepts alongside an EMD example and a variational mode decomposition (VMD) example.

A decomposition gives a representation of the observed signal. Its modes do not automatically identify separate physical sources or isolate noise. The methods guide explains how the methods define their components; the interpretation guide distinguishes numerical convergence, reconstruction, mode diagnostics and evidence for retaining a component.

Guides

Task	Documentation
Understand modes, residues and instantaneous frequency	Introduction
Choose a method and understand its controls	Methods and controls
Organize seismic records and reconstruct a selection	Seismic records
Interpret diagnostics, noise comparisons and selection	Validation and interpretation
Check exact arguments, units and returned fields	Function reference
Find the published work on the methods	Bibliography

EMD example

This signal combines sinusoidal oscillations with a trend. The sifting controls specify the envelope-centering test, the boundary treatment and the iteration limit; they are the configuration of this example.

library(xemd)

Time <- seq(0, 9, length.out = 3000)
Signal <- sin(pi * Time) + sin(2 * pi * Time) + sin(6 * pi * Time) +
    0.5 * Time
Sifting <- list(stopRule = "doubleThreshold", thresholds = c(0.05, 0.5),
                fraction = 0.05, maxSift = 2000, boundary = "reflection",
                maxModes = Inf)
OUT <- decomposeEMD(Signal, sifting = Sifting)

OUT$modes contains the extracted components and OUT$residue contains what remains. Their sum reconstructs the input up to rounding. This additive identity does not establish whether an extracted mode recovers one of the original sinusoids. OUT$converged reports acceptance by the chosen sifting rule, while OUT$stopReason reports why extraction ended. The worked introduction shows those outputs, a reconstruction check and the IMF diagnostics.