{
  "id": "1803.00123",
  "version": "v1",
  "published": "2018-02-28T22:46:00.000Z",
  "updated": "2018-02-28T22:46:00.000Z",
  "title": "On generalized Walsh bases",
  "authors": [
    "Dorin Ervin Dutkay",
    "Gabriel Picioroaga",
    "Sergei Silvestrov"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper continues the study of orthonormal bases (ONB) of $L^2[0,1]$ introduced in \\cite{DPS14} by means of Cuntz algebra $\\mathcal{O}_N$ representations on $L^2[0,1]$. For $N=2$, one obtains the classic Walsh system. We show that the ONB property holds precisely because the $\\mathcal{O}_N$ representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-28T22:46:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized walsh bases",
      "sparse signal recovery",
      "onb property holds",
      "classic walsh system",
      "orthonormal bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}