Kernel-induced sampling theorem for bandpass signals with uniform sampling

In this paper, a sampling theorem for bandpass signals with uniformly spaced sampling points is discussed. We firstly show that a function space consisting of all functions with a specific bandpass property is a reproducing kernel Hilbert space and also give a closed-form of the corresponding reproducing kernel. Moreover, on the basis of the framework of the kernel-induced sampling theorem, we give a simple perfect reconstruction formula for the bandpass signals by uniformly spaced sampling points with the bandpass Nyquist rate, which is defined as twice the signal bandwidth, for the cases that the maximum frequency of the signals is identical to bandwidth multiplied by some positive integer.