{
  "id": "1402.3682",
  "version": "v1",
  "published": "2014-02-15T12:17:05.000Z",
  "updated": "2014-02-15T12:17:05.000Z",
  "title": "Directional time frequency analysis via continuous frame",
  "authors": [
    "Ole Christensen",
    "Brigitte Forster",
    "Peter Massopust"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Grafakos and Sansing \\cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\\mr^n)$ based on Gabor systems in $\\ltr;$ the key tool is the \"ridge idea,\" which lifts a function of one variable to a function of several variables. We generalize their result by showing that similar results hold starting with general frames for $L^2(\\mr),$ both in the setting of discrete frames and continuous frames. This allows to apply the theory for several other classes of frames, e.g., wavelet frames and shift-invariant systems. We will consider applications to the Meyer wavelet and complex B-splines. In the special case of wavelet systems we show how to discretize the representations using $\\epsilon$-nets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-15T12:17:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "42C40",
      "65D07"
    ],
    "keywords": [
      "directional time frequency analysis",
      "continuous frame",
      "similar results hold",
      "complex b-splines",
      "sensitive time-frequency decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.3682C"
    }
  }
}