jsci.maths.wavelet.daubechies8

Class Daubechies8

java.lang.Object

jsci.maths.wavelet.Multiresolution

jsci.maths.wavelet.daubechies8.Daubechies8

All Implemented Interfaces:

NumericalConstants, Filter

public final class Daubechies8
extends Multiresolution
implements Filter, NumericalConstants

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

Field Summary

Fields inherited from interface jsci.maths.NumericalConstants

GAMMA, GOLDEN_RATIO, LOG10, SQRT2, SQRT2PI, TWO_PI

Constructor Summary

Constructors

Constructor and Description
Daubechies8()

Method Summary

Modifier and Type	Method and Description
MultiscaleFunction	dualScaling(int n0, int k)
MultiscaleFunction	dualWavelet(int n0, int k)
double[]	evalScaling(int n0, int k, int j1)
double[]	evalWavelet(int n0, int k, int j1)
int	getFilterType() This method is used to compute how the number of scaling functions changes from on scale to the other.
double[]	highpass(double[] gete) This is the implementation of the highpass Filter.
double[]	highpass(double[] v, double[] param) This is the implementation of the highpass Filter.
double[]	lowpass(double[] gete) This is the implementation of the lowpass Filter.
double[]	lowpass(double[] v, double[] param) This is the implementation of the lowpass Filter.
int	previousDimension(int k) This method return the number of "scaling" functions at the previous scale given a number of scaling functions.
MultiscaleFunction	primaryScaling(int n0, int k)
MultiscaleFunction	primaryWavelet(int n0, int k)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Daubechies8

public Daubechies8()

Method Detail

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.

Specified by:

getFilterType in class Multiresolution

primaryScaling

public MultiscaleFunction primaryScaling(int n0,
                                         int k)

Specified by:

primaryScaling in class Multiresolution

dualScaling

public MultiscaleFunction dualScaling(int n0,
                                      int k)

Specified by:

dualScaling in class Multiresolution

primaryWavelet

public MultiscaleFunction primaryWavelet(int n0,
                                         int k)

Specified by:

primaryWavelet in class Multiresolution

dualWavelet

public MultiscaleFunction dualWavelet(int n0,
                                      int k)

Specified by:

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".

Specified by:

previousDimension in 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.

Specified by:

lowpass in interface Filter

param - a parameter for the filter

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.

Specified by:

highpass in interface Filter

param - a parameter for the filter

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.

Specified by:

lowpass in interface Filter

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.

Specified by:

highpass in interface Filter

evalScaling

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

evalWavelet

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