As of
Mathematica 8, the functionality of the Wavelet Explorer add-on has been integrated into the
Mathematica kernel.
The following is a list of filters available in Wavelet Explorer, along with the equivalent form in
Mathematica 8.
Built-in function equivalents.
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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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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 scaling and wavelet function:
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The functionality of
is now available by using built in function
BSplineBasis:
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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.
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The functionality of
can be replicated as follows:
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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 specifed second argument:
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In
dimension functionality of
can be replicated as follows:
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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.
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| Out[33]= |  |
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The function
can be written as follows:
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. Hence the second derivative comes out to be 0.
