Struct Morlet 

pub struct Morlet { /* private fields */ }

Morlet Wavelet

The Morlet wavelet is a complex exponential multiplied by a Gaussian window. It provides excellent time-frequency localization.

ψ(t) = π^(-1/4) * exp(iω₀t) * exp(-t²/2)

Implementations

impl Morlet

pub fn new(omega0: f64) -> Self

Create a new Morlet wavelet with given central frequency

pub fn with_default_omega() -> Self

Create Morlet wavelet with default ω₀ = 6.0

Trait Implementations

impl Clone for Morlet

fn clone(&self) -> Morlet

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ContinuousWavelet for Morlet

fn wavelet_fft( &self, buffer: &mut [FftComplex<f64>], scale: f64, fft_size: usize, )

Compute Morlet wavelet directly in frequency domain

The Fourier transform of the Morlet wavelet is: Ψ̂(ω) = π^(-1/4) * exp(-(ω - ω₀)²/2) for ω > 0

At scale s, we compute: Ψ̂(s*ω) which shifts the Gaussian peak.

fn admissibility_constant(&self) -> f64

Morlet admissibility constant.

Closed form (analytic approximation for large ω₀): C_ψ = π / ω₀ (single-sided integral ∫₀^∞ |Ψ̂(ω)|²/ω dω for Ψ̂(ω) ∝ exp(−(ω−ω₀)²/2), evaluated by sharp-peak approximation at ω = ω₀, where 1/ω ≈ 1/ω₀).

Empirical match within 1.7% for ω₀=6 (calibrated by icwt(cwt(cos)) at fs=1, n=512, scales 1–200, multiple frequencies — see tests/transforms/cwt_reference.rs). The residual error is the admissibility-correction term exp(−ω₀²/2) contribution, negligible for ω₀ ≥ 5.

fn sst_inversion_constant(&self) -> f64

Morlet SST inversion constant R_ψ = ∫₀^∞ Ψ̂*(ω) dω / ω.

Closed form (analytic approximation for large ω₀): R_ψ ≈ π^{-1/4} · 2π / ω₀ (sharp-peak integral of π^{-1/4}·√(2π)·exp(−(ω−ω₀)²/2) / ω at ω = ω₀, where 1/ω ≈ 1/ω₀). With the next-order 1/ω₀² correction this evaluates to π^{-1/4} · 2π · (1 + 1/(2·ω₀²)) / ω₀ ≈ 0.797 for ω₀=6.

Empirical pure-tone ridge round-trip on Morlet ω₀=6 calibrates to 0.8106, a 1.7% refinement over the closed form that captures the remaining variation of 1/ω across the Gaussian support. Used by crate::transform::sswt_extract_component; with this constant a single-tone SST ridge round-trip on Morlet ω₀=6 reconstructs the input to relative L2 < 0.001 (vs ~0.6 if the CWT admissibility π/ω₀ is used in its place).

Calibration scope. The 0.8106 / 0.7864 ≈ 1.0308 fine-tune factor was calibrated against pure-tone ridge round-trip on Morlet::with_default_omega() (ω₀=6) and is applied uniformly across ω₀. The (ω-ω₀)/ω₀ correction scales similarly across ω₀ values large enough for the analytical approximation to be valid (ω₀ ≥ 5), but for non-default Morlet::new(ω₀) constructions far from ω₀=6 (e.g. ω₀=4 or ω₀=8) the ridge-reconstructed amplitude can drift by a few percent. Same posture as Self::admissibility_constant’s sharp-peak approximation. Acceptable for ridge tracking and IF analysis (which are amplitude-insensitive); document the calibration if you publish reconstructed amplitudes derived from a non-default ω₀.

fn wavelet_function(&self, t: f64, scale: f64) -> Complex<f64>

Get the wavelet function value at position t for scale a

fn center_frequency(&self) -> f64

Get the center frequency of the wavelet

fn bandwidth(&self) -> f64

Get the bandwidth parameter

fn is_complex(&self) -> bool

Check if the wavelet is complex-valued

fn supports_frequency_domain(&self) -> bool

Check if this wavelet supports direct frequency-domain computation

fn wavelet_function_includes_l2_norm(&self) -> bool

Whether wavelet_function already includes the CWT L2 amplitude factor 1/√a in its return value.

fn recommended_scales( &self, signal_length: usize, sampling_freq: f64, ) -> Vec<f64>

Get recommended scale range for a given signal length and sampling frequency

impl Debug for Morlet

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

Formats the value using the given formatter.

impl Default for Morlet

fn default() -> Self

Returns the “default value” for a type.