{
  "annotation_id": "73e8077e-6ac4-4f2a-9f64-a938d0bf8382",
  "date_created": "2026-03-02T18:01:25.020000Z",
  "date_modified": "2026-03-02T18:01:25.020000Z",
  "file_hash": "7ef2c7c9616371baeef35f695a206b15aca584453b7c2b90c55edd0d672ae29e",
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  "record": {
    "abstract": "We demonstrate that the Dirac representation theory can be effectively\nadjusted and applied to signal theory. The main emphasis is on orthogonality as\nthe principal physical requirement. The particular role of the identity and\nprojection operators is stressed. A Dirac space is defined, which is spanned by\nan orthonormal basis labeled with the time points. An infinite number of\northonormal bases is found which are labeled with frequencies, they are\ndistinguished by the continuous parameter a. In a way, similar to one used in\nquantum mechanics, self-adjoint operators (observables) and averages\n(expectation values) are defined. Non orthonormal bases are discussed and it is\nshown, in an example, that they are less stable compared to the orthonormal\nones. A variant of the sampling theorem for finite signals is derived. The\naliasing phenomenon is described in the paper in terms of aliasing symmetry.\nRelations between different bases are derived. The uncertainty principle for\nfinite signals is discussed.",
    "arxiv_id": "physics/9911018",
    "authors": [
      "A. Gersten"
    ],
    "categories": [
      "physics.med-ph",
      "physics.data-an"
    ],
    "doi": "10.1006/aphy.1997.5740",
    "journal_ref": "Annals of Physics (NY) 262, 47-72 (1998)",
    "title": "Dirac\u0027s Representation Theory as a Framework for Signal Theory. I.   Discrete Finite Signals",
    "url": "https://arxiv.org/abs/physics/9911018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "66311dde-e921-406d-93e5-bb7de608223b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}