{
  "annotation_id": "47c7390d-817f-47d6-88a4-7bd4a9e68e4a",
  "date_created": "2026-03-02T18:01:04.162000Z",
  "date_modified": "2026-03-02T18:01:04.162000Z",
  "file_hash": "8940456c6ebdaf66aa2a01c98dafe8f8079d8fc995119a9fb605d05f207b6b6a",
  "private": false,
  "record": {
    "abstract": "Active cancellation of broadband random noise requires the detection of the\nincoming noise with some time advance. In an duct for example this advance must\nbe larger than the delays in the secondary path from the control source to the\nerror sensor. In this paper it is shown that, in some cases, the advance\nrequired for perfect noise cancellation is theoretically infinite because the\ninverse of the secondary path, which is required for control, can include an\ninfinite non-causal response. This is shown to be the result of two mechanisms:\nin the single-channel case (one control source and one error sensor), this can\narise because of strong echoes in the control path. In the multi-channel case\nthis can arise even in free field simply because of an unfortunate placing of\nsensors and actuators. In the present paper optimal feedforward control is\nderived through analytical and numerical computations, in the time and\nfrequency domains. It is shown that, in practice, the advance required for\nsignificant noise attenuation can be much larger than the secondary path\ndelays. Practical rules are also suggested in order to prevent infinite\nnon-causality from appearing.",
    "arxiv_id": "physics/0511163",
    "authors": [
      "Emmanuel Friot"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1016/j.jsv.2005.04.001",
    "title": "Infinite non-causality in active cancellation of random noise",
    "url": "https://arxiv.org/abs/physics/0511163"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "552c9467-f547-41f6-bd1b-63ff2791a0aa",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}