频谱无混叠采样和信号完全可重构采样

通过对采样定理的分析,指出频谱无混叠采样和信号可完全重构采样并不等同,并给出和证明了实现这两个采样的条件,从而全面地回答了在何种条件下,经典采样定理中的最低采样频率可以等于信号最高频率的二倍.作为最低采样频率问题的最典型例子,本文对正弦信号的采样和重构问题作了进一步的分析,揭示了二倍信号频率的采样导致正弦信号相位信息丢失的原因.本文对如何在应用中正确地确定最低采样频率,提供了有益的参考.

Aliasing-Free Sampling and Complete-Reconstruction Sampling

By analyzing the statement of the sampling theorem, it is pointed out that the aliasing-free-in-frequency-domain sampling and complete-reconstruction-in-time-domain sampling are not identical, and different conditions for fulfilling each sampling are formalated. Therefore this paper gives full answers, i.e. the lowest sampling frequency is the twice of the highest signal frequency. This paper analyzes further the sampling and reconstruction of sinusoidal signal since it is a typical situation where the problem of lowest sampling frequency arises, and reveals how the phase information of sinusoidal signal is lost when the sampling frequency is equal to the twice of the signal frequency. Conclusions are also useful in actual applications when the lowest sampling frequency is considered.