MATHEMATICA COMPATIBILITY INFORMATION
Upgrading from:
WaveletExplorer
As of Mathematica 8, the functionality of the Wavelet Explorer add-on has been integrated into the Mathematica kernel.
Wavelet Filters
The following is a list of filters available in Wavelet Explorer, along with the equivalent form in Mathematica 8.
Built-in function equivalents.
To compute wavelet coefficients, use the built-in function WaveletFilterCoefficients.
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Note that all wavelet coefficients are scaled by 
relative to the results from Wavelet Explorer, so to get the equivalent values, you must multiply the result by 
.
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To compute high-pass filter coefficients, use the 
argument to WaveletFilterCoefficients.
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Scaling and Wavelet Functions
The following is a list of functions available in Wavelet Explorer, along with the equivalent form in Mathematica 8.
| ScalingFunction[filt,j] | WaveletPhi[wave] |
| Wavelet[wave,j] | WaveletPsi[wave] |
| ShannonPhi[t] | WaveletPhi[ShannonWavelet[lim],t] |
| ShannonPsi[t] | WaveletPsi[ShannonWavelet[lim],t] |
| MeyerPhi[n,t,lim] | WaveletPhi[MeyerWavelet[n,lim],t] |
| MeyerPsi[n,t,lim] | WaveletPsi[MeyerWavelet[n,lim],t] |
| SplinePhi[n,t,lim] | WaveletPhi[BattleLemarieWavelet[n,lim],t] |
| SplinePsi[n,t,lim] | WaveletPsi[BattleLemarieWavelet[n,lim],t] |
| BSpline[n,t] | BSplineBasis[{n,{u1,u2,...}},0,t] |
| DScalingFunction[filt,jmax,m] | Dt[WaveletPhi[wave,t],{t,m}] |
| DWavelet[filt,jmax,m] | Dt[WaveletPsi[wave,t],{t,m}] |
Built-in function equivalents.
The functionality of 
is now available by using WaveletPhi.
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To find the derivative of the scaling function, use Dt and WaveletPhi.
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The functionality of 
is now available by using Dt and WaveletPsi.
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Compute higher-order derivatives of the scaling and wavelet function.
The InterpolatingFunction outputted from WaveletPhi and WaveletPsi has InterpolationOrder set to 
. Hence the second derivative comes out to be 0.
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Resampling and interpolating with a higher InterpolationOrder resolves the issue.
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The functionality of 
is now available by using the built-in function BSplineBasis.
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Wavelet Transforms
The following is a list of wavelet transforms available in Wavelet Explorer, along with the equivalent form in Mathematica 8.
| WaveletTransform[data,filt,j] | DiscreteWaveletTransform[data,wave,j] |
| InverseWaveletTransform[wd,filt] | InverseWaveletTransform[dwd] |
| WaveletPacketCoefficients[data,filt,j] | DiscreteWaveletPacketTransform[data,filt,j] |
| WaveletPacketTransform[data,filt,l] | WaveletBestBasis[DiscreteWaveletPacketTransform[...]] |
| InverseWaveletPacketTransform[wpdata,filt] | InverseWaveletTransform[dwd] |
Built-in function equivalents. The function
is not directly supported with built-in functionality.
The functionality of 
is now available by using DiscreteWaveletTransform.
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To compute a packet transform, use DiscreteWaveletPacketTransform.
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Use InverseWaveletTransform to compute the inverse:
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The functionality of 
can be replicated as follows.
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Sine & Cosine Transforms
The following is a list of functions available in Wavelet Explorer, along with the equivalent form in Mathematica 8.
Built-in function equivalents. The functions
,
,
,
,
,
,
, and
are not directly supported with built-in functionality.
To compute 
, use the built-in function FourierDST.
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with a specified second argument.
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In one dimension, the functionality of 
can be replicated as follows.
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Similarly, we can write 
using FourierDCT.
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Other Utilities
The following is a list of functions available in Wavelet Explorer, along with the equivalent form in Mathematica 8.
Built-in function equivalents. The functions
and
are not directly supported with built-in functionality.
To plot wavelet coefficients, use WaveletScalogram.
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Use WaveletThreshold for data compression.
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The function 
can be written as follows.
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