Periodically Nonuniform Sampling and Reconstruction of Signals in Function Spaces Associated with the Linear Canonical Transform

In practice, we are given only a finite number of samples. Sampling theorems with slow-decayed synthesizing functions, therefore, may not be suitable for perfect reconstruction of a signal. Focusing on this issue, we investigate the reconstruction of a periodically nonuniform sampled signal in function spaces associated with the linear canonical transform (LCT). We propose a sampling theorem in which compactly supported synthesizing functions can be guaranteed by the existence of finite impulse response perfect reconstruction filter banks associated with the LCT. We also present the simulation results to validate our algorithm.