Sampling Theorems of Band-limited Signals in the Linear Canonical Transform Domain

The linear canonical transform(LCT) has become a very active area in signal processing community in recent years, with many applications in optics, radar system analysis, filter design, phase retrieval, pattern recognition, etc. Many well-known transforms such as the Fourier transform,the fractional Fourier transform,and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper, the band-limited sampling theorems and reconstruction formulas for linear canonical transformed signals are derived . The previously developed sampling theorems in Fourier domain or fractional Fourier domain are shown to be special cases of the achieved results.Finally, an example of sampling a chirp signal is given, which demonstrate that a signal can be sampled without aliasing at a rate less than the Nyquist rate by using the sampling theorem for the LCT.