Module transform 

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
• Hilbert spectrum / HHT: EMD-family instantaneous energy density over time and frequency
• EWT: Spectrum-adaptive Meyer filter bank — components sum exactly to the signal; useful when EMD-style adaptivity is wanted with wavelet-frame perfect reconstruction
• SST/SSWT: Synchrosqueezed Wavelet Transform — reassigns CWT energy onto an instantaneous-frequency axis for sharp ridges with provable AM-FM convergence (Daubechies-Lu-Wu 2011)

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 ceemdan::CEEMDAN;

pub use ceemdan::CeemdanVariant;

pub use complex_wavelets::ComplexMexicanHat;

pub use complex_wavelets::ComplexMorlet;

pub use complex_wavelets::ComplexPaul;

pub use cwt::CWTResult;

pub use cwt::ContinuousWavelet;

pub use cwt::MexicanHat;

pub use cwt::Morlet;

pub use cwt::cwt;

pub use cwt::cwt_fft;

pub use cwt::icwt;

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::DWTResult;

pub use dwt::MultilevelDWTResult;

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 emd::EEMD;

pub use emd::EMDConfig;

pub use emd::EMDResult;

pub use emd::EndEffectStrategy;

pub use emd::IMF;

pub use emd::emd;

pub use emd::hilbert_transform;

pub use ewt::BoundaryDetection;

pub use ewt::EWTConfig;

pub use ewt::EWTResult;

pub use ewt::GammaStrategy;

pub use ewt::SpectrumPreproc;

pub use ewt::ewt;

pub use ewt::iewt;

pub use hilbert_spectrum::HilbertSpectrum;

pub use hilbert_spectrum::HilbertSpectrumConfig;

pub use hilbert_spectrum::hilbert_spectrum;

pub use matrix2d::Matrix2D;

pub use memd::DirectionStrategy;

pub use memd::MEMDConfig;

pub use memd::MEMDResult;

pub use memd::memd;

pub use modwt::MODWTResult;

pub use modwt::MultilevelMODWTResult;

pub use modwt::imodwt;

pub use modwt::imodwt_multilevel;

pub use modwt::max_modwt_level;

pub use modwt::modwt;

pub use modwt::modwt_into;

pub use modwt::modwt_level_into;

pub use modwt::modwt_multilevel;

pub use modwt::modwt_multilevel_into;

pub use sswt::GreedyRidgeConfig;

pub use sswt::SSWTConfig;

pub use sswt::SSWTPlan;

pub use sswt::SSWTPlanMemoryMode;

pub use sswt::SSWTPlanOptions;

pub use sswt::SSWTResult;

pub use sswt::sswt;

pub use sswt::sswt_extract_component;

pub use sswt::sswt_extract_ridge;

pub use sswt::sswt_into;

pub use swt::MultilevelSWTResult;

pub use swt::SWTResult;

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 vmd::AlphaSpec;

pub use vmd::ModeInitialization;

pub use vmd::VMDConfig;

pub use vmd::VMDResult;

pub use vmd::VmdRedundancy;

pub use vmd::VmdSelectKConfig;

pub use vmd::VmdSelectKResult;

pub use vmd::vmd;

pub use vmd::vmd_select_k;

pub use wpt::CostFunction;

pub use wpt::NodeId;

pub use wpt::WPNode;

pub use wpt::WPTConfig;

pub use wpt::WPTResult;

pub use wpt::best_basis;

pub use wpt::iwpt;

pub use wpt::wpt;

Modules

boundary

ceemdan

Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)

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

ewt

Empirical Wavelet Transform (EWT).

hilbert_spectrum

Hilbert spectral analysis — the second half of the Hilbert-Huang Transform.

matrix2d

Flat row-major 2D matrix used by transform results.

memd

Multivariate Empirical Mode Decomposition (MEMD).

modwt

simd

SIMD-accelerated wavelet transforms.

sswt

Synchrosqueezed Wavelet Transform (SST / SSWT).

swt

vmd

Variational Mode Decomposition (VMD).

wpt

Wavelet Packet Transform (WPT) and Inverse WPT

Structs

TransformConfig

Configuration for wavelet transforms

Functions

max_decomposition_level

Calculate the maximum decomposition level for a signal (DWT with downsampling)

max_decomposition_level_with_boundary

Boundary-aware variant of max_decomposition_level.

max_shift_invariant_level

Calculate the maximum decomposition level for shift-invariant transforms (MODWT/SWT)