关于正弦信号Nyquist采样的一个注记

A note on sampling the sinusoidal signal with Nyquist rate

讨论正弦信号的Nyquist率采样问题 .对于正弦信号 ,一般认为以Nyquist率对其均匀采样 ,至少在一定条件下 ,所得采样序列即可完全包含原信号信息 ,并能精确重构原信号 .但从频域混叠的角度讲 ,Nyquist率采样在正弦信号的特殊情况下 ,是不符合采样定理要求的 ,故采用频域分析方法对Nyquist采样时的频谱混叠现象进行了分析 ,澄清了关于正弦信号Nyquist采样问题的认识 .

Discussion on sampling the sinusoidal signal with Nyquist rate is presented. Let f(t)= A sin(2π f 0 t+φ) be the general form of sinusoidal signal, and f(nT s)= A sin(2π f 0 nT s+φ) the uniformly sampling of f(t) with Nyquist rate of f s= 2f 0 (i.e. the sampling space T s= 1/f s= 1/2f 0 ). It is generally considered that the sequence f(nT s) contains all the information about f(t),and that, at least, within certain constraints, f(t) can be uniquely reconstructed from f(nT s). However, from the view of point of frequency overlap, sampling the sinusoidal signal with Nyquist rate violates the demand of the sampling theorem. A thorough analysis of this problem in frequency domain is presented, and a correction of the aforementioned conclusion is given.