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ContinuousWavelet

oxiphysics_core::wavelets

Struct ContinuousWavelet 

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pub struct ContinuousWavelet;
Expand description

Continuous wavelet transform (CWT) with multiple mother wavelets.

Supports Morlet, Mexican Hat (Ricker), and Paul wavelets for scalogram computation and instantaneous frequency estimation.

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impl ContinuousWavelet

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pub fn morlet(t: f64, sigma: f64) -> f64

Evaluate the (real part of the) Morlet wavelet at position t.

sigma controls the time-frequency trade-off (bandwidth parameter).

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pub fn mexican_hat(t: f64, sigma: f64) -> f64

Evaluate the Mexican-hat (Ricker) wavelet at position t.

Defined as (1 - t²/σ²) exp(-t²/2σ²).

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pub fn paul(t: f64, m: u32) -> f64

Evaluate the Paul wavelet of order m at position t.

The real part is proportional to cos(m * atan2(t, 1)) / (1 + t²)^((m+1)/2).

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pub fn cwt_morlet(signal: &[f64], dt: f64, scales: &[f64]) -> Vec<Vec<f64>>

Compute the CWT scalogram using the Morlet wavelet.

Returns a matrix scalogram[scale_idx][time_idx] where each row corresponds to one entry in scales.

  • signal — input time series.
  • dt — sampling interval.
  • scales — desired wavelet scales (dilation parameters).
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pub fn cwt_mexican_hat(signal: &[f64], dt: f64, scales: &[f64]) -> Vec<Vec<f64>>

Compute the CWT scalogram using the Mexican-hat wavelet.

Returns a matrix scalogram[scale_idx][time_idx].

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pub fn cwt_paul( signal: &[f64], dt: f64, scales: &[f64], m: u32, ) -> Vec<Vec<f64>>

Compute the CWT scalogram using the Paul wavelet of order m.

Returns a matrix scalogram[scale_idx][time_idx].

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pub fn instantaneous_frequency( scalogram: &[Vec<f64>], scales: &[f64], dt: f64, ) -> Vec<f64>

Estimate the instantaneous dominant frequency at each time step from a scalogram.

For each time index, finds the scale with maximum CWT coefficient magnitude and converts it to a frequency via f = 1 / (scale * dt).

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pub fn scale_averaged_power( scalogram: &[Vec<f64>], scales: &[f64], ) -> Vec<(f64, f64)>

Compute total power at each scale (integrate over time).

Returns a vector of (scale, power) pairs.

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