{
  "method": "MVMD",
  "slug": "mvmd",
  "title": "MVMD: share mode frequencies across multiple channels",
  "summary": "MVMD couples channel-specific mode spectra through shared center frequencies. The modes can have different amplitudes and phases in each channel.",
  "steps": [
    {
      "title": "Align the channels",
      "text": "Supply measurements on a common time grid and prepare their mirrored spectra."
    },
    {
      "title": "Update channel spectra",
      "text": "Each channel fits a mode around the current shared center."
    },
    {
      "title": "Pool spectral energy",
      "text": "Update each center using the spectral energy from all channels, then repeat."
    },
    {
      "title": "Recover mode stacks",
      "text": "Invert the spectra and retain the (mode,time,channel) organization before application-specific grouping."
    }
  ],
  "parameters": [
    {
      "name": "K and alpha",
      "effect": "The teaching run uses three modes and bandwidth penalty 1500."
    },
    {
      "name": "Upstream trace settings",
      "effect": "Uniform initialization, tau=0, and max_iter=60 bound this PySDKit demonstration; not all are public DeTime parameters."
    },
    {
      "name": "primary_period / mode groups",
      "effect": "Controls DeTime's assignment of the returned modes to output components."
    }
  ],
  "cautions": [
    "The optional backend requires aligned multichannel input and an explicitly checked axis convention.",
    "PySDKit's all-axis FFT shift changes the internal channel order; its final inverse shift restores input order. The animation applies that same restoration to every displayed iterate.",
    "A shared mode center does not identify a shared causal source, and tau=0 can leave reconstruction error."
  ],
  "references": [
    {
      "title": "PySDKit MVMD interface and implementation",
      "url": "https://pysdkit.readthedocs.io/en/stable/API/pysdkit._vmd.html"
    },
    {
      "title": "Multivariate variational mode decomposition",
      "url": "https://doi.org/10.1109/TSP.2019.2951223"
    }
  ],
  "trace_kind": "upstream execution trace",
  "trace_note": "Captured PySDKit 0.5.0 joint solver arrays on input shaped (channel,time). Internal channels correspond to input indexes [2, 0, 1] (zero-based); applying indexes [1, 2, 0] restores original order in every displayed spectrum and mode. The final trace is checked against the upstream returned modes.",
  "input_note": "Deterministic synthetic teaching signal; not a benchmark.",
  "example_config": {
    "method": "MVMD",
    "params": {
      "K": 3,
      "alpha": 1500.0,
      "primary_period": 24
    },
    "backend": "python"
  },
  "checks": {
    "captured_final_iteration": 18,
    "trace_matches_upstream_modes": 1.8490349884547896e-07,
    "mode_sum_rmse": 0.05570209440280112,
    "backend_version": "0.5.0",
    "internal_channel_input_indexes": [
      2,
      0,
      1
    ],
    "output_channel_permutation": [
      1,
      2,
      0
    ],
    "finite_trace": true
  },
  "source_files": [
    "src/detime/methods/mvmd.py"
  ],
  "frames": 32,
  "duration_ms": 12050,
  "poster_frame": 15,
  "width": 1280,
  "height": 820,
  "artifacts": {
    "gif": {
      "file": "mvmd.gif",
      "bytes": 419913,
      "sha256": "32619e36a8e1a296dc46cdf9c85818f476f9c49a463b22d8b13efea16c0e05b1"
    },
    "poster": {
      "file": "mvmd.png",
      "bytes": 191673,
      "sha256": "9a7171d5f66eab1c0489e69167168e6ecb43a99555d8858909209b8c7fd06cd8"
    },
    "data": {
      "file": "mvmd.npz",
      "bytes": 250939,
      "sha256": "585b033414568d6f0e1feb3c571d70c088c4e001dad04176926d15528c6fbf9e"
    }
  },
  "source_arrays": {
    "time": [
      144
    ],
    "input_channels": [
      144,
      3
    ],
    "frequency_grid": [
      288
    ],
    "iteration_ids": [
      8
    ],
    "mode_spectra": [
      8,
      288,
      3,
      3
    ],
    "internal_mode_spectra": [
      8,
      288,
      3,
      3
    ],
    "shared_centers": [
      19,
      3
    ],
    "input_order_mode_trace": [
      8,
      3,
      144,
      3
    ],
    "internal_channel_input_indexes": [
      3
    ],
    "output_channel_permutation": [
      3
    ],
    "upstream_returned_modes": [
      3,
      144,
      3
    ]
  },
  "render_provenance": {
    "python_version": "3.11.3",
    "dependencies": {
      "numpy": "2.4.6",
      "scipy": "1.17.1",
      "statsmodels": "0.15.0",
      "matplotlib": "3.11.2",
      "Pillow": "13.0.0",
      "PyWavelets": "1.9.0",
      "EMD-signal": "1.10.0",
      "vmdpy": "0.2",
      "PySDKit": "0.5.0"
    },
    "source_hashes": {
      "scripts/generate_method_animations.py": "f62989af55a7e48495c24afcfee31751d3785e5f78bb4b900bef23a429deaa84",
      "scripts/method_animations/adaptive.py": "7d728d88b4ba1a8dd82890c7a6b017d542728b50dc477c281e9bbfcbae164a1d",
      "scripts/method_animations/common.py": "73ad7e8b4e5b67f87d13e59adab2c93e983fe1aaf06ee627d22cb7c7e696016a",
      "src/detime/backends.py": "7432dcf59e382580dfb32f1f57e61ff71a30567c049b35243e24e3644523eda6",
      "src/detime/core.py": "d95b348cd8b16b56d18840965579c947a11628d969dd6c32c4af7723f5a027f4",
      "src/detime/methods/mvmd.py": "3e66ea12f131795eeb5ebbb24bd6affe7bfc104ac94ef7d8cdeaff6073413fd7",
      "src/detime/registry.py": "e934ffca17880cefe5add728aa497e63ea811d7ae43abec1ea498de718094066"
    }
  }
}