Signal Processing ToolSet小波分析工具一问

              
      
在LabVIEW的Signal Processing Toolset工具包中，启动安装后的示例程序，即
Start>>Programs>>National Instruments>>Signal Processing Toolset>>
NI SPT Start-Up，在进行小波包设计时的"Wavelets and Filters"窗口，有8张Graph
图，分别为Analysis Scaling, Analysis Wavelet, Analysis Lowpass, Analysis
Highpass, Synthesis Scaling, Synthesis Wavelet, Synthesis Lowpass, Synthesis
Highpass.
我的问题是：Scaling函数和Lowpass的系数、Wavelet函数和Highpass系数有什么对应
关系吗？刚开始我以为Lowpass的系数就是Scaling函数在相应横坐标的值，即Lowpass
系数就是Scaling函数离散化后的几个点，但是仔细比较，Scaling函数离散化后的值
和Lowpass系数还是有不同的。Lowpass和Highpass系数与Scaling和Wavelet函数有什么
关系呢？
Wavelets and Filters窗口见附图。
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Thank you for your question about SPT!
First, I should mention you that it's not for wavelet packets, but for wavelets.
The wavelet transform can be implemented by the inner product of the signal and
the wavelet functions, and you can also implement it with the efficient Mallat
algorithm, which uses the low-pass and high pass filter banks. The filtering
procedure includes not only the convolution but also the down-sampling. So it's
obvious the low-pass or high-pass filters are not the scaling or wavelet functions. But the filters are from the functions. You also can get the functions from the filters. You can check a function named "Mother Wavelet ans Scaling Function.vi", which is used to get the scaling function and wavelet function under certain scale(decomposition level). It can be implemented as following:
1. Input a pulse sequence into the wavelet coefficients of a certain level
2. Set all the other wavelet (or approximation) coefficients to zeros
3. Reconstruct the signal, then the signal is the wavelet or scaling functions
corresponding to that decomposition level.
Hope this can be helpful for your question!
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多谢！
回答很详细，不胜感激！
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You are welcome!
Hope you can evoke more question about SPT and it will help us make it better.
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不好意思，按照你的步骤重构Scaling Function or Wavelet Function时碰到点问题。
利用Inverse Discrete Wavelet Transform Ex (Windows).vi重构函数时，脉冲序列
是作为Nth scale approximation coefficients，还是作为Nth scale detail
coefficients？ 假如作为scale detail coefficients，Nth scale approximation
coefficients置为0吧？脉冲序列的长度有限定吗？
synthesis filters参数利用例子程序中的Synthesis Filters的全局变量
(Global Variable)吧？
还有一个问题，我对例子进行测试，当Filter系数点数为4，Refinement为1时，得到
的Function数据点数为6。Refinement为2，Function点数为12......，这样递增上去的。
是否脉冲长度应取为3？
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Please use the Easy Discrete Wavelet Transform.vi and the inverse one.
Input a all zero series;
apply the wavelet decomposition;
extract the approximation (for scaling) or detail (for wavelet) coefficients under the largest scale;
replace the center value with 1;
apply the reconstruction.
Then you can get the scaling function or wavelet function under any scale.
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