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"]

Wavelet Explorer
 In[14]:=
 Out[14]=

 In[13]:=
 Out[13]=

Wavelet Explorer
 In[2]:=
 Out[2]=

### 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}]

ScalingFunction 的功能可以用 WaveletPhi 实现：

Wavelet Explorer
 In[17]:=
 Out[17]=

Wavelet Explorer
 In[2]:=
 Out[2]=

DWavelet 的功能可用 DtWaveletPsi 实现：

Wavelet Explorer
 In[2]:=
 Out[2]=

 In[1]:=

WaveletPhiWaveletPsi 输出的 InterpolatingFunctionInterpolationOrder 设为 1. 因此第二个导数为0.

 In[2]:=
 Out[2]=
 In[3]:=
 Out[3]=

Wavelet Explorer
 In[5]:=
 Out[5]=
 In[6]:=
 Out[6]=

BSpline 的功能可以用内置函数 BSplineBasis 实现：

Wavelet Explorer
 In[2]:=
 In[3]:=
 Out[3]=

### 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]

WaveletTransform 功能可用 DiscreteWaveletTransform 实现：

Wavelet Explorer
 In[18]:=
 Out[18]=

Wavelet Explorer
 In[2]:=
 Out[2]=

Wavelet Explorer
 In[4]:=
 Out[4]=

MRDecomposition 的功能可以编写如下：

Wavelet Explorer
 In[2]:=
 In[3]:=
 Out[3]=
 In[4]:=
 Out[4]=

### 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]

Wavelet Explorer
 In[10]:=
 Out[10]=

Wavelet Explorer
 In[2]:=
 Out[2]=

SinPacketCoefficients 的一维功能可以编写如下：

Wavelet Explorer
 In[2]:=
 In[3]:=
 Out[3]=

Wavelet Explorer
 In[5]:=
 In[6]:=
 Out[6]=

### 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]

Wavelet Explorer
 In[30]:=
 Out[30]=
 In[33]:=
 Out[33]=

Wavelet Explorer
 In[2]:=
 In[3]:=
 Out[3]=
 In[4]:=
 Out[4]=

Wavelet Explorer
 In[2]:=
 In[3]:=
 In[4]:=
 Out[4]=
 In[5]:=
 Out[5]=