#### Title

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

#### 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 2*σ*(Nyquist rate) and 3*σ*, 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.

#### Recommended Citation

Wu, Yan.
2007.
"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

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/680