Hilbert Transform Associated with the Linear Canonical Transform
Hilbert Transform Associated with the Linear Canonical Transform
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发表时间：
2006
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通讯作者：
Li Bing-zhao;Tao Ran
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作者：
Li Bing-zhao;Tao Ran
希尔伯特变换（HT）是一种重要的信号处理工具，在信号处理中的调制、边缘检测和滤波器设计等许多应用中都有使用。HT将解析信号与其原始信号连接起来。同时，线性正则变换（LCT）是傅里叶变换和分数阶傅里叶变换的推广形式，可以认为是一般的线性变换。线性正则变换域中希尔伯特变换的定义和性质 给出了这类希尔伯特变换的一些重要性质,并表明新定义的希尔伯特变换与传统傅里叶变换域中的希尔伯特变换具有一些相似的性质。
Hilbert transform(HT) is an important signal processing tool that is used in many applications such as modulations,edge detection and filter design in signal processing.An analytic signal and its original signal are connected by the HT.At the same time,the linear canonical transform(LCT) is the generalized form of Fourier transform and the fractional Fourier transform,it can be considered as a general linear transform.The definition and properties of Hilbert transform in linear canonical transform domain were proposed.Some important properties of this kind of Hilbert transform were given,and it is shown that the newly defined Hilbert transform has some similar properties with the Hilbert transform in the traditional Fourier transform domain.