Struct ComplexMexicanHat 

pub struct ComplexMexicanHat {
    pub omega0: f64,
}

Complex Mexican Hat (Ricker) Wavelet

A complex version of the Mexican Hat wavelet, excellent for detecting singularities and discontinuities in financial data such as jumps, crashes, or sudden volatility changes.

Mathematical form: ψ(t) = (1 - t²) * exp(-t²/2) * exp(iω₀t)

Fields

omega0: f64

Central frequency parameter

Implementations

impl ComplexMexicanHat

pub fn new(omega0: f64) -> Self

Create a new Complex Mexican Hat wavelet

pub fn for_jump_detection() -> Self

Create version optimized for jump detection in financial data

Trait Implementations

impl Clone for ComplexMexicanHat

fn clone(&self) -> ComplexMexicanHat

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ContinuousWavelet for ComplexMexicanHat

fn admissibility_constant(&self) -> f64

ComplexMexicanHat admissibility constant.

Empirical fit: C_ψ = 3π / (ω₀ + √2)^{3/2}, where ω₀ + √2 is the wavelet’s spectral peak (matching center_frequency()). Matches calibration within ~3% for ω₀ ∈ [4, 8] and within ~7% for ω₀=3 — see test_admissibility_calibration_spread_stays_bounded in tests/transforms/cwt_reference.rs for the sweep.

Depends on the 2.0.0 admissibility correction added to wavelet_function (subtracts ω₀²·exp(−ω₀²/2)·exp(−η²/2) so Ψ̂(0) = 0). Without that correction the Calderón integral diverges and no finite C_ψ exists; this formula is only valid for the corrected wavelet.

Limitations:

• For ω₀ ≤ 2, the correction term is comparable in magnitude to the wavelet itself; reconstruction becomes strongly signal-dependent.
• At very low signal frequencies relative to ω₀ (e.g. f·n < 8 for ω₀ ≥ 6), the dominant CWT scale runs out of the typical scale grid’s coverage — the empirical reconstruction underestimates by tens of percent at the slowest frequency.

Use ComplexMorlet or ComplexPaul for amplitude-correct reconstruction at the most extreme parameter combinations.

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 wavelet_function_includes_l2_norm(&self) -> bool

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

fn supports_frequency_domain(&self) -> bool

Check if this wavelet supports direct frequency-domain computation

fn sst_inversion_constant(&self) -> f64

Synchrosqueezing inversion constant R_ψ = ∫₀^∞ Ψ̂*(ω) dω / ω, used by crate::transform::sswt_extract_component to recover an EMD-like component from an SST ridge.

fn wavelet_fft( &self, _buffer: &mut [FftComplex<f64>], _scale: f64, _fft_size: usize, )

Compute the wavelet directly in frequency domain (if supported)

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 ComplexMexicanHat

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

Formats the value using the given formatter.

impl Default for ComplexMexicanHat

fn default() -> Self

Returns the “default value” for a type.