WaveForM block: reconstruct wavelet bands

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How it works

Method maturity: experimental. Implementation: python.

The implemented operator delegates the transform to PyWavelets. It reconstructs the coarsest approximation as trend and selected detail arrays as season, then derives the residual by subtraction. The animation exposes the analysis filter taps, coefficient arrays and inverse reconstructions. The WaveForM and WaveletMixer identifiers have different default wavelets and selected bands; neither operator runs the cited complete forecasting backbone.

Deterministic synthetic teaching signal; not a benchmark.

Open GIF · Static PNG · Source arrays (NPZ) · Trace metadata

Follow the four steps

1. Analyze with fixed wavelet filters

PyWavelets applies the selected analysis filters to produce approximation and detail coefficients at several resolutions.

2. Reconstruct the approximation

Keep only the coarsest approximation coefficients, zero the other coefficient arrays and apply inverse reconstruction to obtain the trend.

3. Reconstruct selected detail bands

Keep the explicitly selected coefficient-list positions and reconstruct their combined sample-aligned contribution as season.

4. Inspect the remaining detail

The residual is the observed input minus the approximation and selected details. All displayed components match the public operator.

Parameters that change the result

Parameter	Effect on the computation
wavelet	Selects the fixed analysis/synthesis wavelet family; db4 and sym4 are used by these two examples.
level	Requests decomposition depth, limited by the implementation using the input length and filter length.
season_levels	Contains coefficient-list positions: 1 denotes cD_L, 2 denotes cD_(L-1), and so on; position 0 is the trend approximation.

What this animation computes

Intermediate arrays are computed with the implemented operator helpers. The final trend, season and residual are checked against public decompose(). The animation explains this standalone experimental block; its source architecture is cited for provenance.

Interpretation

• WaveForM's graph enhancement and WaveletMixer's trained mixing layers are outside these standalone operators.
• The source uses PyWavelets' default symmetric boundary extension; boundary values depend on that convention.
• A selected frequency-scale band is called season by the common result contract; periodic interpretation requires separate evidence.
• The coefficient heatmap pads unequal-length arrays with zeros for display only. Computation uses their original lengths.

Try the method

Use this configuration with DecompositionConfig and decompose. The animation generator supplies the teaching input and records intermediate arrays.

{
  "method": "WAVEFORM_BLOCK",
  "params": {
    "wavelet": "db4",
    "level": 3,
    "season_levels": [
      1,
      2
    ]
  },
  "backend": "python"
}

See the configuration reference for the full interface and optional dependencies.

Sources and reproduction

• Implemented DeTime operator
• Yang et al. (2023), WaveForM: Graph Enhanced Wavelet Learning for Long Sequence Forecasting of Multivariate Time Series
• DeTime implementation: src/detime/methods/neural_blocks/neural_block_portfolio.py

Regenerate this animation with python scripts/generate_method_animations.py --methods WAVEFORM_BLOCK. The reproduction guide explains the environment, numerical checks, coverage manifest, and how to inspect the stored arrays.