A Pyramidal Haar-Transform Implementation

  • Luigi Carrioli


The one-dimensional Haar functions set, used to built the homonymous transform, is defined in the interval (0,1) in this way:
$$\begin{gathered} \begin{array}{*{20}{c}} p \\ {HAR\left( {2 + n,x} \right) = } \end{array}\left[ {\begin{array}{*{20}{c}} {{2^{p/2}} for \frac{n}{{{2^p}}} \leqslant X < \frac{{\left( {n + 1/2} \right)}}{{{2^p}}}} \\ { - {2^{p/2}} for \frac{{\left( {n + 1/2} \right)}}{{{2^p}}} \leqslant X < \frac{{n + 1}}{{{2^p}}}} \\ {0 elsewhere} \end{array}} \right. \hfill \\ p = 1,2, \ldots n = 0,1, \ldots ,{2^p} - 1 \hfill \\ \end{gathered} $$




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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Luigi Carrioli
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaPavia UniversityPaviaItaly

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