Real clifford windowed Fourier transform
Real clifford windowed Fourier transform
复制标题
DOI：
10.1007/s10114-011-9655-0
复制
发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
M. Bahri;S. Adji;Ji Man Zhao
中科院分区：
文献类型：
--
作者：
M. Bahri;S. Adji;Ji Man Zhao
我们在Clifford分析的框架下研究窗口傅里叶变换，我们称之为Clifford窗口傅里叶变换（CWFT）。基于Clifford Fourier变换（CFT）的谱表示，导出了CFT的移位、调制、重构公式、正交关系、等距性和再生核等重要性质。我们还提出了一个例子来显示经典的加窗傅里叶变换（WFT）和CWFT之间的差异。最后，作为应用，我们建立了CWFT的Heisenberg型测不准原理。
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.