Struct ComplexMorlet 

pub struct ComplexMorlet {
    pub omega0: f64,
    pub bandwidth: f64,
}

Enhanced Complex Morlet Wavelet for Financial Analysis

The complex Morlet wavelet provides excellent time-frequency localization and is particularly useful for analyzing non-stationary financial time series.

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

Parameters

• omega0: Central frequency parameter (typically 5-6 for good localization)
• bandwidth: Controls time-frequency trade-off

Financial Properties

• Preserves phase information for trend direction analysis
• Optimal for detecting frequency modulations in price data
• Excellent for identifying regime changes through instantaneous frequency

Fields

omega0: f64

Central frequency parameter (ω₀)

bandwidth: f64

Bandwidth parameter for time-frequency localization

Implementations

impl ComplexMorlet

pub fn new(omega0: f64, bandwidth: f64) -> Self

Create a new Complex Morlet wavelet

Arguments

• omega0 - Central frequency parameter (recommended: 5-6)
• bandwidth - Bandwidth parameter (recommended: 1.0-2.0)

Examples

use iron_wave::transform::complex_wavelets::ComplexMorlet;
let wavelet = ComplexMorlet::new(6.0, 1.0);

pub fn for_finance() -> Self

Create Complex Morlet with optimal parameters for financial analysis

Uses ω₀ = 6.0 and bandwidth = 1.0 for good time-frequency localization suitable for most financial time series analysis.

pub fn for_hft() -> Self

Create Complex Morlet optimized for high-frequency trading analysis

Uses higher ω₀ = 8.0 for better frequency resolution to capture rapid price movements in HFT data.

pub fn for_regime_detection() -> Self

Create Complex Morlet optimized for regime detection

Uses lower ω₀ = 4.0 for better time localization to detect sudden regime changes.

pub fn admissibility_constant(&self) -> f64

Get the admissibility constant for reconstruction

pub fn instantaneous_frequency(&self, scale: f64, sampling_freq: f64) -> f64

Compute instantaneous frequency at a given time and scale

Trait Implementations

impl Clone for ComplexMorlet

fn clone(&self) -> ComplexMorlet

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ContinuousWavelet for ComplexMorlet

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 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 ComplexMorlet

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

Formats the value using the given formatter.

impl Default for ComplexMorlet

fn default() -> Self

Returns the “default value” for a type.