buildHilbertSpectrum: Hilbert Spectrum by Frequency Cells

In xemd: eXtended Empirical Mode Decomposition

Hilbert Spectrum by Frequency Cells

Description

Accumulates the instantaneous amplitude, or its square, of every mode in the frequency cell of its instantaneous frequency, sample by sample, and integrates the result over time.

Usage

buildHilbertSpectrum(frequency, amplitude, edges, exponent, samplingInterval)

Arguments

frequency	Numeric matrix, samples by modes, of instantaneous frequencies in Hz, finite or NA.
amplitude	Finite non-negative matrix with the dimensions of frequency, the instantaneous amplitudes in the units of the signal.
edges	At least two finite, strictly increasing cell edges in Hz; cell b is [e_b, e_{b+1}). Negative values are admitted. No default.
exponent	The power p: 1 for the amplitude spectrum, 2 for the spectrum weighted by squared amplitude. No default.
samplingInterval	Sampling interval \Delta t in seconds, a finite number greater than zero.

Details

The spectrum holds the mass of each cell,

H[n, b] = \sum_{k:\, f_k[n] \in [e_b, e_{b+1})} a_k[n]^p,

in units of the signal to the power p. A frequency outside the edges or NA adds nothing. The marginal spectrum of a cell is the time integral \Delta t \sum_n H[n, b]. No scaling or division by the cell width is applied: the values are masses, not densities. The inputs are usually the frequency and amplitude of computeInstantaneousAttributes.

Value

A list with

spectrum	Double matrix, samples by cells, in units of the signal to the power p.
marginal	Numeric vector by cell, in units of the signal to the power p times seconds.

See Also

computeInstantaneousAttributes, decomposeEMD

Examples

Time <- seq(0, 9, length.out = 3000)
Signal <- sin(pi * Time) + sin(2 * pi * Time) + sin(6 * pi * Time) +
    0.5 * Time
Modes <- decomposeEMD(Signal,
                      sifting = list(stopRule = "doubleThreshold"))$modes
Attributes <- computeInstantaneousAttributes(Modes,
                                             samplingInterval = 9 / 2999)
OUT <- buildHilbertSpectrum(Attributes$frequency, Attributes$amplitude,
                            edges = c(1, 2, 3, 4, 5), exponent = 2,
                            samplingInterval = 9 / 2999)
dim(OUT$spectrum)
OUT$marginal

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