A proof on the minimum and permissible sampling rates for the first-order sampling of bandpass signals ?
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 2? (Nyquist rate) and 3?, where ? 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.
permissible sampling rates first-order sampling bandpass signals nyquist rate csinc interpolation sampling theory