Sampling and reconstruction of bandpass signal

A bandpass signal is also a kind of band-limited signal. If it is sampled according to Shannon sampling theorem, a too high sampling rate would be required. Since the spectrum of the bandpass signal confined to two bands symmetrically located about zero and vanishes outside, it can be sampled at a rate less than the Nyquist rate. A further study based on time-frequency equivalence is carried out, and a sampling theorem for a bandpass signal with sufficient sampling condition to avoid “aliasing” and the reconstruction formula in an almost everywhere convergence sense is obtained. Finally a comparison to Shannon sampling theorem is given