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# Class JSci.maths.wavelet.daubechies8.Daubechies8

    java.lang.Object
       |
       +----JSci.maths.wavelet.Multiresolution
               |
               +----JSci.maths.wavelet.daubechies8.Daubechies8

public final class Daubechies8
extends Multiresolution
implements Filter, NumericalConstants

Daubechies wavelets adapted to the interval by Meyer. Thanks to Pierre Vial for the filters.

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filtretype
minlength

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Daubechies8()

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dualScaling(int, int)
dualWavelet(int, int)
evalScaling(int, int, int)
evalWavelet(int, int, int)
getFilterType()
  This method is used to compute how the number of scaling functions changes from on scale to the other.
highpass(double[])
  This is the implementation of the highpass Filter.
highpass(double[], double[])
  This is the implementation of the highpass Filter.
lowpass(double[])
  This is the implementation of the lowpass Filter.
lowpass(double[], double[])
  This is the implementation of the lowpass Filter.
previousDimension(int)
  This method return the number of "scaling" functions at the previous scale given a number of scaling functions.
primaryScaling(int, int)
primaryWavelet(int, int)

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filtretype

     protected static final int filtretype

minlength

     protected static final int minlength

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Daubechies8

     public Daubechies8()

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getFilterType

     public int getFilterType()

  This method is used to compute how the number of scaling functions changes from on scale to the other. Basically, if you have k scaling function and a Filter of type t, you'll have 2*k+t scaling functions at the next scale (dyadic case). Notice that this method assumes that one is working with the dyadic grid while the method "previousDimension" define in the interface "Filter" doesn't.

  Overrides:
    getFilterType in class Multiresolution

primaryScaling

     public MultiscaleFunction primaryScaling(int n0,
                                              int k)

  Overrides:
    primaryScaling in class Multiresolution

dualScaling

     public MultiscaleFunction dualScaling(int n0,
                                           int k)

  Overrides:
    dualScaling in class Multiresolution

primaryWavelet

     public MultiscaleFunction primaryWavelet(int n0,
                                              int k)

  Overrides:
    primaryWavelet in class Multiresolution

dualWavelet

     public MultiscaleFunction dualWavelet(int n0,
                                           int k)

  Overrides:
    dualWavelet in class Multiresolution

previousDimension

     public int previousDimension(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". It is used by the interface "Filter".

  Overrides:
    previousDimension in class Multiresolution

lowpass

     public double[] lowpass(double v[],
                             double param[])

  This is the implementation of the lowpass Filter. It is used by the interface "Filter". Lowpass filters are normalized so that they preserve constants away from the boundaries.

highpass

     public double[] highpass(double v[],
                              double param[])

  This is the implementation of the highpass Filter. It is used by the interface "Filter". Highpass filters are normalized in order to get L2 orthonormality of the resulting wavelets (when it applies). See the class DiscreteHilbertSpace for an implementation of the L2 integration.

lowpass

     public double[] lowpass(double gete[])

  This is the implementation of the lowpass Filter. It is used by the interface "Filter". Lowpass filters are normalized so that they preserve constants away from the boundaries.

highpass

     public double[] highpass(double gete[])

  This is the implementation of the highpass Filter. It is used by the interface "Filter". Highpass filters are normalized in order to get L2 orthonormality of the resulting wavelets (when it applies). See the class DiscreteHilbertSpace for an implementation of the L2 integration.

evalScaling

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

evalWavelet

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

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