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# Class JSci.maths.wavelet.Cascades

    java.lang.Object
       |
       +----JSci.maths.AbstractMath
               |
               +----JSci.maths.wavelet.Cascades

public final class Cascades
extends AbstractMath

This class is a standard implementation of the Cascades algorithm.

##

dimension(int, int)
  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have.
dimension(int, int, int)
  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have.
dimensionHaar(int, int)
  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have.
doublesample(double[])
  Method used to oversample according to the Haar transform
evalScaling(Filter, int, int, int)
evaluation(Filter, int, double[])
evalWavelet(Filter, int, int, int)
evalWavelet(Filter, int, int, int, int)
evalWaveletHaar(Filter, int, int, int)
evalWaveletQuadratic(Filter, int, int, int)
oversample(double[])
  method used to oversample according to the lazy (Dirac Delta Function) interpolation
PowerOf2(int)
previousDimension(int, int)
  This method return the number of "scaling" functions at the previous scale given a number of scaling functions.
quadraticOversample(double[])
  Special oversampling for the quadratic spline interpolation
supersample(double[])
  Special oversampling for the linear spline interpolation

##

previousDimension

     public static int previousDimension(int filtretype,
                                         int k)

  This method return the number of "scaling" functions at the previous scale given a number of scaling functions. The answer is always smaller than the provided value (about half since this is a dyadic implementation). This relates to the same idea as the "filter type".

evalScaling

     public static double[] evalScaling(Filter filtre,
                                        int n0,
                                        int j1,
                                        int k)

evalWavelet

     public static double[] evalWavelet(Filter filtre,
                                        int filtretype,
                                        int n0,
                                        int j1,
                                        int k)

evalWavelet

     public static double[] evalWavelet(Filter filtre,
                                        int n0,
                                        int j1,
                                        int k)

evalWaveletHaar

     public static double[] evalWaveletHaar(Filter filtre,
                                            int n0,
                                            int j1,
                                            int k)

evalWaveletQuadratic

     public static double[] evalWaveletQuadratic(Filter filtre,
                                                 int n0,
                                                 int j1,
                                                 int k)

PowerOf2

     public static int PowerOf2(int pwrOf2)

oversample

     public static double[] oversample(double data[])

  method used to oversample according to the lazy (Dirac Delta Function) interpolation

doublesample

     public static double[] doublesample(double data[])

  Method used to oversample according to the Haar transform

supersample

     public static double[] supersample(double data[])

  Special oversampling for the linear spline interpolation

quadraticOversample

     public static double[] quadraticOversample(double v[])

  Special oversampling for the quadratic spline interpolation

dimension

     public static int dimension(int n0,
                                 int jfin,
                                 int filtertype)

  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have. (Dyadic multiresolutions of type filtretype.)

  Parameters:
    filtertype - filter type
    n0 - number of scaling functions initially
    jfin - number of iterations

dimension

     public static int dimension(int n0,
                                 int jfin)

  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have. (Linear spline and dyadic multiresolution of type 1.)

  Parameters:
    n0 - number of scaling functions initially
    jfin - number of iterations

dimensionHaar

     public static int dimensionHaar(int n0,
                                     int jfin)

  Starting with n0 scaling functions and going jfin scales ahead (iterating jfin times), tells you how many scaling functions you'll have. (Haar and dyadic multiresolution of type 0.)

  Parameters:
    n0 - number of scaling functions initially
    jfin - number of iterations

evaluation

     public static double[] evaluation(Filter filtre,
                                       int j1,
                                       double init[])

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