Module dual_tree_cwt 

Dual-Tree Complex Wavelet Transform (DT-CWT)

The Dual-Tree Complex Wavelet Transform provides near shift-invariance and directional selectivity by using two real DWTs in parallel to construct complex wavelet coefficients.

Key Features

• Shift Invariance: Approximately shift-invariant (unlike standard DWT)
• Directional Selectivity: Can distinguish between +45° and -45° features
• Perfect Reconstruction: Exact reconstruction of original signal
• Low Redundancy: Only 2:1 redundancy (vs 100:1+ for CWT)
• Efficient: O(N) complexity like standard DWT

Mathematical Foundation

The DT-CWT uses two separate DWT trees with carefully designed filters:

• Tree A: Real part of complex coefficients
• Tree B: Imaginary part of complex coefficients

The complex coefficients are: c[n] = c_a[n] + i * c_b[n]

Financial Applications

• Trend Analysis: Directional selectivity for uptrends vs downtrends
• Volatility Clustering: Shift-invariant detection of volatile periods
• Regime Detection: Robust to time-shifts in regime boundaries
• Multi-Scale Analysis: Complex coefficients preserve phase relationships

Structs

DTCWTConfig

Dual-Tree Complex Wavelet Transform Configuration

DTCWTResult

Result of Dual-Tree Complex Wavelet Transform

DirectionalAnalysis

Directional analysis result for financial applications

DualTreeCWT

Dual-Tree CWT implementation

Enums

FirstLevelFilter

First-level filter options for DT-CWT