A Proof on the Minimum and Permissible Sampling Rates for the First-Order Sampling of Bandpass Signals
Digital Signal Processing
In this paper, we present a rigorous mathematical proof on the minimum sampling rate as well as all acceptable sampling rates (independent of band position) for the first-order sampling of bandpass signals. It is shown that the minimum sampling rate is between 2σ(Nyquist rate) and 3σ, where σ is the bandwidth of a bandpass signal. It is also noted that the Nyquist rate is actually an asymptotic sampling rate for the first-order sampling of bandpass signals. A so-called csinc interpolator is used in the reconstruction of a bandpass signal from its samples, which makes the sampling theorem for bandpass signals congruent with the sampling theorem for lowpass signals.
"A Proof on the Minimum and Permissible Sampling Rates for the First-Order Sampling of Bandpass Signals."
Digital Signal Processing, 17 (4): 848-854.
doi: 10.1016/j.dsp.2007.02.008 source: https://www.sciencedirect.com/science/article/pii/S105120040700022X?via%3Dihub