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.