Struct HilbertSpectrum 

#[non_exhaustive]
pub struct HilbertSpectrum {
    pub density: Vec<Vec<f64>>,
    pub frequencies: Vec<f64>,
    pub sample_rate: f64,
}

Joint time-frequency-energy density h(t, ω) built from an EMDResult’s IMFs.

Indexing: density[t][k] is the summed squared Hilbert amplitude of every IMF whose instantaneous frequency lies in bin k at sample t. The bin centers are in Self::frequencies.

Fields (Non-exhaustive)

Non-exhaustive structs could have additional fields added in future. Therefore, non-exhaustive structs cannot be constructed in external crates using the traditional Struct { .. } syntax; cannot be matched against without a wildcard ..; and struct update syntax will not work.

density: Vec<Vec<f64>>

density[t][k] — energy in freq bin k at sample t.

frequencies: Vec<f64>

Frequency bin centers in Hz, length num_freq_bins.

sample_rate: f64

Sample rate that the original signal was measured at, in Hz.

Implementations

impl HilbertSpectrum

pub fn marginal(&self) -> Vec<f64>

Marginal Hilbert spectrum h(ω) = Σ_t h(t, ω). Length = frequencies.len(). Huang 1998 §VI.

pub fn instantaneous_energy(&self) -> Vec<f64>

Instantaneous energy density E(t) = Σ_k h(t, ω_k). Length = density.len().

pub fn degree_of_stationarity(&self) -> Vec<f64>

Degree of stationarity DoS(ω) = (1/T) Σ_t (1 − h(t, ω) / mean_t h(t, ω))² per Huang 1998 Eq 8.6. Length = frequencies.len().

A pure tone gives DoS ≈ 0 at the bin where its energy lives; a chirp or FM signal gives much larger values across every bin it visits. Frequency bins that are empty for the whole record return 0.0 rather than NaN.

Discretization caveat for whole-signal comparisons. A bin that receives energy at only a single time sample (an edge artifact, or a chirp’s brief visit) yields the extreme value DoS = N − 1 — so the raw peak DoS does not separate stationary from non-stationary inputs on its own. To compare whole signals, weight by the marginal:

<DoS> = (Σ_ω marginal(ω) · DoS(ω)) / Σ_ω marginal(ω)

which suppresses the sparse outliers and recovers Huang 1998 §VI’s qualitative ordering.

Trait Implementations

impl Clone for HilbertSpectrum

fn clone(&self) -> HilbertSpectrum

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for HilbertSpectrum

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.