WOLFRAM 语言兼容性信息

# WaveletExplorer

Mathematica 8 中，Wavelet Explorer 附加程序包的功能已被集成到 Mathematica 内核.

### 小波滤波器

 HaarFilter[] WaveletFilterCoefficients[HaarWavelet[]] DaubechiesFilter[n] WaveletFilterCoefficients[DaubechiesWavelet[n]] LeastAsymmetricFilter[n] WaveletFilterCoefficients[SymletWavelet[n]] CoifletFilter[n] WaveletFilterCoefficients[CoifletWavelet[n]] ShannonFilter[lim] WaveletFilterCoefficients[ShannonWavelet[lim]] MeyerFilter[n,lim] WaveletFilterCoefficients[MeyerWavelet[n,lim]] SplineFilter[n,lim] WaveletFilterCoefficients[BattleLemarieWavelet[n,lim]] BiorthogonalSplineFilter[n,m] WaveletFilterCoefficients[BiorthogonalSplineWavelet[n,m]] HighpassFilter[h] WaveletFilterCoefficients[wave,"PrimalHighpass"]

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### 尺度和小波函数

 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}]

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WaveletPhiWaveletPsi 输出的 InterpolatingFunctionInterpolationOrder 设为 . 因此第二个导数为0.

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### 小波变换

 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]

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### 正弦和余弦变换

 CosTransform[data,n, BasisType->m] FourierDCT[data,m] SinTransform[data,n,BasisType->m] FourierDST[data,m] InverseCosTransform[cdata] FourierDCT[cdata,m] InverseSinTransform[sdata] FourierDST[sdata,m]

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### 其它应用

 PlotCoefficients[wd] WaveletListPlot[dwd] PhaseSpacePlot[wd] WaveletScalogram[dwd] ShowBasisPosition[wd] DiscreteWaveletData[…]["BestBasisBlockView"] PlotCoefficients2D[wd] WaveletMatrixPlot[dwd] ShowBasisPosition2D[wd] DiscreteWaveletData[…]["BestBasisBlockView"] WaveletCompress[wd,…] WaveletThreshold[dwd,tspec]

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