Expand description
Wavelet transform implementations
This module provides various wavelet transform algorithms:
§Transform Comparison
| Transform | Shift-Invariant | Downsampling | Filter Scaling | Reconstruction |
|---|---|---|---|---|
| DWT | No | Yes (by 2) | None | Perfect |
| MODWT | Yes | No | 1/√2 | Perfect |
| SWT | Yes | No | None | Averaging |
§When to Use Each Transform
- DWT: Fast, memory-efficient, good for compression and denoising
- MODWT: Best for time series analysis, variance/volatility estimation
- SWT: Compatible with MATLAB/PyWavelets, good for shift-invariant analysis
§See Also
- Wavelet families and recommended choices:
docs/WAVELET_FAMILIES.md - Detailed transform behavior (DWT/MODWT/SWT/WPT/CWT/EMD):
docs/TRANSFORMS_GUIDE.md - High-level user guide for choosing transforms:
docs/USER_GUIDE.md
Re-exports§
pub use boundary::BoundaryMode;pub use complex_wavelets::ComplexMexicanHat;pub use complex_wavelets::ComplexMorlet;pub use complex_wavelets::ComplexPaul;pub use cwt::cwt;pub use cwt::cwt_fft;pub use cwt::icwt;pub use cwt::CWTResult;pub use cwt::ContinuousWavelet;pub use cwt::MexicanHat;pub use cwt::Morlet;pub use dual_tree_cwt::DTCWTConfig;pub use dual_tree_cwt::DTCWTResult;pub use dual_tree_cwt::DirectionalAnalysis;pub use dual_tree_cwt::DualTreeCWT;pub use dual_tree_cwt::FirstLevelFilter;pub use dwt::dwt;pub use dwt::dwt_multilevel;pub use dwt::dwt_multilevel_into;pub use dwt::idwt;pub use dwt::idwt_multilevel;pub use dwt::idwt_multilevel_into;pub use dwt::DWTResult;pub use dwt::MultilevelDWTResult;pub use emd::emd;pub use emd::EMDConfig;pub use emd::EMDResult;pub use emd::EEMD;pub use emd::IMF;pub use modwt::imodwt;pub use modwt::imodwt_multilevel;pub use modwt::max_modwt_level;pub use modwt::modwt;pub use modwt::modwt_multilevel;pub use modwt::modwt_multilevel_into;pub use modwt::MODWTResult;pub use modwt::MultilevelMODWTResult;pub use swt::iswt;pub use swt::iswt_multilevel;pub use swt::swt;pub use swt::swt_multilevel;pub use swt::swt_multilevel_into;pub use swt::MultilevelSWTResult;pub use swt::SWTResult;pub use wpt::best_basis;pub use wpt::iwpt;pub use wpt::wpt;pub use wpt::CostFunction;pub use wpt::NodeId;pub use wpt::WPNode;pub use wpt::WPTConfig;pub use wpt::WPTResult;
Modules§
- boundary
- complex_
wavelets - Complex Wavelets Module
- cwt
- dual_
tree_ cwt - Dual-Tree Complex Wavelet Transform (DT-CWT)
- dwt
- emd
- Empirical Mode Decomposition (EMD) for non-stationary signal analysis
- modwt
- simd
- SIMD-accelerated wavelet transforms for x86/x86_64 architectures
- swt
- wpt
- Wavelet Packet Transform (WPT) and Inverse WPT
Structs§
- Transform
Config - Configuration for wavelet transforms
Functions§
- max_
decomposition_ level - Calculate the maximum decomposition level for a signal (DWT with downsampling)
- max_
shift_ invariant_ level - Calculate the maximum decomposition level for shift-invariant transforms (MODWT/SWT)