Struct MexicanHat 

pub struct MexicanHat { /* private fields */ }

Mexican Hat (Ricker) Wavelet

The Mexican Hat wavelet is the negative normalized second derivative of a Gaussian function. It’s real-valued and symmetric.

ψ(t) = (2/(√3σ π^(1/4))) * (1 - t²/σ²) * exp(-t²/2σ²)

Implementations

impl MexicanHat

pub fn new(sigma: f64) -> Self

Create a new Mexican Hat wavelet with given width parameter

pub fn with_default_sigma() -> Self

Create Mexican Hat wavelet with default σ = 1.0

Trait Implementations

impl Clone for MexicanHat

fn clone(&self) -> MexicanHat

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ContinuousWavelet for MexicanHat

fn admissibility_constant(&self) -> f64

Mexican Hat admissibility constant.

Closed form: C_ψ = (4√π / 3) · σ. The σ factor comes from the L2-normalized wavelet’s FT-scaling property: for ψ_σ(t) = (1/√σ)·ψ(t/σ), the FT is Ψ̂_σ(ω) = √σ · Ψ̂(σω), so |Ψ̂_σ(ω)|² = σ · |Ψ̂(σω)|² and under the substitution u = σω the admissibility integral becomes ∫₀^∞ |Ψ̂_σ(ω)|²/ω dω = σ · ∫₀^∞ |Ψ̂(u)|²/u du = σ · (4√π/3).

For the canonical σ=1, this matches the previous value of 4√π/3 ≈ 2.363 (empirical match within 0.3%). For σ ≠ 1, this gives σ·(4√π/3) — important for MexicanHat::new(σ) with non-default width, where the previous σ-invariant formula made icwt reconstruct at ~σ× gain.

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 MexicanHat

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

Formats the value using the given formatter.

impl Default for MexicanHat

fn default() -> Self

Returns the “default value” for a type.