Hilbert transform associated with the linear canonical transform

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 analytical signal and its original signal are connected by HT. At the same time, the linear canonical transform (LCT) is the generalized form of Fourier transform and fractional Fourier transform, it can be considered as a general linear transform. The definition and properties of HT in LCT domain were proposed. Some important properties of this kind of HT were given, and it is shown that the newly defined HT has some similar properties with the HT in the traditional Fourier transform domain.