{
  "annotation_id": "ee6cdc13-ff71-42b6-a995-11806a1e62c6",
  "date_created": "2026-03-02T18:01:25.025000Z",
  "date_modified": "2026-03-02T18:01:25.025000Z",
  "file_hash": "308c3db6137afd6e6d59516d4b4a9fe2a0d406b6519cb50946451858c343f45c",
  "private": false,
  "record": {
    "abstract": "We generalize previous results and demonstrate that the Dirac representation\ntheory can be effectively adjusted and applied to continuous or discrete\nsignals of infinite time duration. The role of the identity and projection\noperators is emphasized. The sampling theorem is viewed from the point of view\nof orthogonal physical states. An orthogonal basis which spanned the time\nspace, ceases to be orthogonal and becomes overcomplete if the domain of\nfrequencies is restricted in a bandwidth. In this case there exists an infinite\nnumber of sub-bases of discrete times which are orthogonal and complete. The\nrelation between the overcomplete bases and a complete one is the essence of\nthe sampling theorem. The signal theory is reformulated in the framework of the\nDirac bra-kets. The case of signals existing for positive time is treated in\ndetail.",
    "arxiv_id": "physics/9911019",
    "authors": [
      "A. Gersten"
    ],
    "categories": [
      "physics.med-ph",
      "physics.data-an"
    ],
    "doi": "10.1006/aphy.1997.5741",
    "journal_ref": "Annals of Physics (NY) 262, 73-104 (1998)",
    "title": "Dirac\u0027s Representation Theory as a Framework for Signal Theory. II.   Infinite Duration and Continuous Signals",
    "url": "https://arxiv.org/abs/physics/9911019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c1a6d295-dc27-4300-94f8-10b41063ec44",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}