{
  "method": "WAVELET",
  "slug": "wavelet",
  "title": "Wavelets: filter, downsample, and reconstruct selected scales",
  "summary": "A discrete wavelet transform separates scales through paired low-pass and high-pass filters. DeTime reconstructs selected coefficient blocks onto the original sample grid.",
  "steps": [
    {
      "title": "Choose the filter bank",
      "text": "The wavelet fixes the analysis and synthesis filters; this trace uses db4."
    },
    {
      "title": "Build the pyramid",
      "text": "Low-pass and high-pass filtering are followed by decimation; repeat on the approximation."
    },
    {
      "title": "Select coefficient blocks",
      "text": "Retain a block, zero the others, and apply the inverse transform to obtain a sample-aligned contribution."
    },
    {
      "title": "Assign outputs",
      "text": "This example assigns A3 to trend and D3+D2 to season; the remainder is input minus those outputs."
    }
  ],
  "parameters": [
    {
      "name": "wavelet",
      "effect": "Controls filters and their support; db4 has eight analysis taps."
    },
    {
      "name": "level",
      "effect": "Controls pyramid depth; the example uses three levels."
    },
    {
      "name": "trend_levels / season_levels",
      "effect": "Indexes the wavedec list [A3,D3,D2,D1] here, not ascending physical scales."
    },
    {
      "name": "Boundary convention",
      "effect": "The current wrapper uses PyWavelets' default symmetric mode."
    }
  ],
  "cautions": [
    "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."
  ],
  "references": [
    {
      "title": "PyWavelets discrete transform",
      "url": "https://pywavelets.readthedocs.io/en/stable/ref/dwt-discrete-wavelet-transform.html"
    },
    {
      "title": "Inverse transform and partial reconstruction",
      "url": "https://pywavelets.readthedocs.io/en/stable/ref/idwt-inverse-discrete-wavelet-transform.html"
    },
    {
      "title": "Signal-extension modes",
      "url": "https://pywavelets.readthedocs.io/en/stable/ref/signal-extension-modes.html"
    }
  ],
  "trace_kind": "upstream numerical stages",
  "trace_note": "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.",
  "input_note": "Deterministic synthetic teaching signal; not a benchmark.",
  "example_config": {
    "method": "WAVELET",
    "params": {
      "wavelet": "db4",
      "level": 3,
      "trend_levels": [
        0
      ],
      "season_levels": [
        1,
        2
      ]
    }
  },
  "checks": {
    "all_band_reconstruction_max_abs_error": 1.7763568394002505e-15,
    "pyramid_matches_wavedec": 0.0
  },
  "source_files": [
    "src/detime/methods/wavelet.py"
  ],
  "frames": 32,
  "duration_ms": 12050,
  "poster_frame": 15,
  "width": 1280,
  "height": 820,
  "artifacts": {
    "gif": {
      "file": "wavelet.gif",
      "bytes": 226237,
      "sha256": "76e2029cd628c60a7542df8b9f8feb9aea7ac7292aabaa556c46cc94a63290c2"
    },
    "poster": {
      "file": "wavelet.png",
      "bytes": 194914,
      "sha256": "4ea9def42c329cabb85e3ca79d5c381510a93cd08942a19c7d8b4ca742d8597c"
    },
    "data": {
      "file": "wavelet.npz",
      "bytes": 14888,
      "sha256": "ee04357085b42f960e622d1c70bc071f1afae4e1c9884d585dc326c7fa440f82"
    }
  },
  "source_arrays": {
    "time": [
      192
    ],
    "input": [
      192
    ],
    "analysis_lowpass": [
      8
    ],
    "analysis_highpass": [
      8
    ],
    "reconstructed_bands": [
      4,
      192
    ],
    "approximation_0": [
      192
    ],
    "approximation_1": [
      99
    ],
    "approximation_2": [
      53
    ],
    "approximation_3": [
      30
    ],
    "detail_1": [
      99
    ],
    "detail_2": [
      53
    ],
    "detail_3": [
      30
    ]
  },
  "render_provenance": {
    "python_version": "3.12.14",
    "dependencies": {
      "numpy": "2.3.5",
      "scipy": "1.17.0",
      "statsmodels": "0.15.0",
      "matplotlib": "3.10.8",
      "Pillow": "12.3.0",
      "PyWavelets": "1.10.0",
      "EMD-signal": "1.10.0",
      "vmdpy": "0.2",
      "PySDKit": "0.5.0"
    },
    "source_hashes": {
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      "scripts/method_animations/adaptive.py": "7d728d88b4ba1a8dd82890c7a6b017d542728b50dc477c281e9bbfcbae164a1d",
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      "src/detime/core.py": "d95b348cd8b16b56d18840965579c947a11628d969dd6c32c4af7723f5a027f4",
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      "src/detime/registry.py": "e934ffca17880cefe5add728aa497e63ea811d7ae43abec1ea498de718094066"
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  }
}