A Proof on the Minimum and Permissible Sampling Rates for the First-Order Sampling of Bandpass Signals

Yan WuFollow

Document Type

Article

Publication Date

7-2007

Publication Title

Digital Signal Processing

DOI

10.1016/j.dsp.2007.02.008

ISSN

1051-2004

Abstract

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.

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