WaveletPlot - Maple Help

DiscreteTransforms

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

 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:

$\mathrm{\phi }\left(x\right)=\sum _{n=1}^{\mathrm{rtable_elems}\left(h\right)}{h}_{n}\mathrm{\phi }\left(2x-n\right)$

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

$\mathrm{\psi }\left(x\right)=\sum _{n=1}^{\mathrm{rtable_elems}\left(g\right)}{g}_{n}\mathrm{\phi }\left(2x-n\right)$

 The functions phi are then plotted using plots[listplot].
 • h and g are usually the high and low pass scaling coefficients.

Examples

 > $\mathrm{with}\left(\mathrm{DiscreteTransforms}\right):$

The command to create the plot from the Plotting Guide is

 > $\mathrm{WaveletPlot}\left(\mathrm{WaveletCoefficients}\left("Daubechies",4\right)\right)$
 > $\mathrm{WaveletPlot}\left(\mathrm{WaveletCoefficients}\left("Daubechies",4\right),\mathrm{output}=\mathrm{mother}\right)$
 > $\mathrm{WaveletPlot}\left(\mathrm{WaveletCoefficients}\left("Daubechies",4\right),\mathrm{output}=\mathrm{father}\right)$
 > $\mathrm{WaveletPlot}\left(\mathrm{WaveletCoefficients}\left("Symlet",4\right),\mathrm{minpoints}=300,\mathrm{waveletname}="Sym4"\right)$