R/transformEWT.R

In xemd: eXtended Empirical Mode Decomposition

# Adapted from ewtpy, revision f9ff38bc5cd7859eea58c5b29099f8a503792b63.
# SPDX-License-Identifier: MIT
# Copyright (c) 2019 Vinícius Carvalho & Eduardo Mazoni
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# Mirror extension of the EWT record and its DFT
# (descomposicion.model.es.qmd:117-121), with the convention of ewtpy EWT1D:
# for h = ceiling(N / 2), the samples x_{h-1}, ..., x_1 precede the record and
# x_{N-1}, ..., x_{N-h} follow it, so T = N + 2h - 1. observed holds the
# positions h, ..., h + N - 1 of the record inside the extension. The
# convention is EWT's own, distinct from the VMD extension of
# .transformReflection.
.transformEWT <- function(signal) {
    n <- length(signal)
    h <- ceiling(n / 2)
    list(spectrum = stats::fft(signal[c(rev(seq_len(h - 1)), seq_len(n),
                                        (n - 1):(n - h))]),
         observed = h - 1 + seq_len(n))
}