Windowed Fourier transform of two-dimensional quaternionic signals
Windowed Fourier transform of two-dimensional quaternionic signals
复制标题
DOI：
10.1016/j.amc.2010.03.082
复制
发表时间：
2010-06
期刊：
影响因子：
--
通讯作者：
M. Bahri;E. Hitzer;R. Ashino;R. Vaillancourt
中科院分区：
文献类型：
--
作者：
M. Bahri;E. Hitzer;R. Ashino;R. Vaillancourt
在本文中，我们推广了经典的窗口傅里叶变换（WFT）的四元数值信号，称为四元数窗口傅里叶变换（QWFT）。利用四元数傅里叶变换的谱表示，我们得到了几个重要的性质，如重建公式，再生核，等距，正交关系。以高斯函数为窗函数，得到了四元数Gabor滤波器，它在四元数Gabor基上分解信号时起系数函数的作用。我们应用QWFT的性质和（右侧）QFT建立一个海森堡型QWFT的不确定性原理。最后，我们简要介绍了QWFT在线性时变系统中的应用。
In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued signals, called the quaternionic windowed Fourier transform (QWFT). Using the spectral representation of the quaternionic Fourier transform (QFT), we derive several important properties such as reconstruction formula, reproducing kernel, isometry, and orthogonality relation. Taking the Gaussian function as window function we obtain quaternionic Gabor filters which play the role of coefficient functions when decomposing the signal in the quaternionic Gabor basis. We apply the QWFT properties and the (right-sided) QFT to establish a Heisenberg type uncertainty principle for the QWFT. Finally, we briefly introduce an application of the QWFT to a linear time-varying system.