Frames in linear canonical transform domain

The frame theory is one of the fundamental tools in study the sampling questions, epically for non-uniform sampling questions, in signal processing community. Weyl-Heisenberg frames are foundation of Gabor transform, Short time Fourier transform, and proved to be important tools in time-frequency signal processing, it gives a signal's local properties by using these frames to present a signal. Extensions of these frames are obtained in the linear canonical transform domains from the frames in the time-frequency domain, properties of frames in linear canonical transform domains are also derived.