Complete Identification of Permissible Sampling Rates for the First- Order Sampling of Multi-Band Bandpass Signals

The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the permissible sampling rates, a necessary and sufficient sampling theorem for multi-band bandpass signals is presented in terms of a series of csinc-interpolators. Key-Words: Multi-band bandpass signals, Sampling theorem, First-order sampling, Nyquist rate, Permissible sampling rates, Aliasing, csinc-interpolation