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Wavelet decomposition

Wavelet decomposition

Property Value
Method WAVELET
Input mode univariate
Trend shape (96,)
Notebook execution ran
Reconstruction RMSE 0.00000000

Notebook example metric: root mean square of input - (trend + season + residual) over all samples and channels. This checks additive bookkeeping; it is not a forecast error or a component-recovery score. The separate teaching input and intermediate arrays for the animation are linked below.

How it works

Method maturity: stable. Implementation: wrapper.

A discrete wavelet transform separates scales through paired low-pass and high-pass filters. DeTime reconstructs selected coefficient blocks onto the original sample grid.

WAVELET: Choose the filter bank; Build the pyramid; Select coefficient blocks; Assign outputs

Deterministic synthetic teaching signal; not a benchmark.

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

Follow the four steps

1. Choose the filter bank

The wavelet fixes the analysis and synthesis filters; this trace uses db4.

2. Build the pyramid

Low-pass and high-pass filtering are followed by decimation; repeat on the approximation.

3. Select coefficient blocks

Retain a block, zero the others, and apply the inverse transform to obtain a sample-aligned contribution.

4. Assign outputs

This example assigns A3 to trend and D3+D2 to season; the remainder is input minus those outputs.

Parameters that change the result

Parameter Effect on the computation
wavelet Controls filters and their support; db4 has eight analysis taps.
level Controls pyramid depth; the example uses three levels.
trend_levels / season_levels Indexes the wavedec list [A3,D3,D2,D1] here, not ascending physical scales.
Boundary convention The current wrapper uses PyWavelets' default symmetric mode.

What this animation computes

Computed with PyWavelets 1.10.0; inverse band reconstructions call the current DeTime helper. Moving filter support is a labeled illustration; coefficient values are actual library outputs.

Interpretation

  • Wavelet detail coefficients are decimated and should not be mistaken for sample-aligned output curves.
  • Assigning scales to trend or season is an application choice; the transform does not identify physical mechanisms.
  • The animation uses a safe fixed depth; excessive levels make boundary effects dominate.

Try the method

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

{
  "method": "WAVELET",
  "params": {
    "wavelet": "db4",
    "level": 3,
    "trend_levels": [
      0
    ],
    "season_levels": [
      1,
      2
    ]
  }
}

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

Sources and reproduction

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

Code

case = CASES["WAVELET"]
run_gallery_case("WAVELET")

Output

WAVELET: Wavelet-based decomposition exposed through the common output contract.
status: ran
input mode: univariate
trend shape: (96,)
backend: python
reconstruction RMSE: 0.00000000

Decomposition Plot

WAVELET decomposition