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DiscreteTransforms

  

WaveletPlot

  

plot the mother wavelet and the father wavelet (the scaling function) from the scaling and wavelet coefficients

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

WaveletPlot(g, h, options);

Parameters

g

-

Vector; the scaling coefficients of the wavelet

h

-

Vector; the wavelet coefficients of the wavelet

options

-

(optional) equation(s) of the form keyword = value, where keyword is output, waveletname, or minpoints 

Options

• 

output=both, mother, or father

– 

Determines whether the mother wavelet, father wavelet (the scaling function), or both are plotted.

– 

The default value of this option is both.

• 

minpoints=posint 

– 

Determines the minimum number of points sampled. Higher values will result in more detailed plots.

– 

The default value of this option is 200.

• 

waveletname=string 

– 

Determines the plot labels.

– 

The default value of this option is the empty string.

– 

If this option is provided, the plots will be indexed by "waveletname Father wavelet" and "waveletname Mother wavelet".

Description

• 

WaveletPlot plots the scaling function and the mother wavelet given Vectors of the scaling and wavelet coefficients of a wavelet.

• 

This function uses the Cascades algorithm to approximate a function phi(x) satisfying the equation:

φx=n=1rtable_elemshhnφ2xn

  

phi is the scaling function. From phi, the wavelet psi is computed as

ψx=n=1rtable_elemsggnφ2xn

  

The functions phi are then plotted using plots[listplot].

• 

h and g are usually the high and low pass scaling coefficients.   

Examples

withDiscreteTransforms:

The command to create the plot from the Plotting Guide is

WaveletPlotWaveletCoefficientsDaubechies,4

WaveletPlotWaveletCoefficientsDaubechies,4,output=mother

WaveletPlotWaveletCoefficientsDaubechies,4,output=father

WaveletPlotWaveletCoefficientsSymlet,4,minpoints=300,waveletname=Sym4

See Also

DiscreteWaveletTransform

InverseDiscreteWaveletTransform

Wavelet Examples and Applications

WaveletCoefficients

Wavelets

 


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