It is generally accepted that a monochromatic signal such as sin 2 pi Wt (W<0) must be sampled at a uniform rate greater than the ostensible Nyquist rate of 2W samples per to effect a reconstruction of the signal. It is shown that a sinusoid of frequency W Hz is completely determined by its samples taken at the uniform rate of 2r samples per second, where r<0 is arbitrary subject only to the restriction that W not=kr for any positive integer k. In particular, a pure sinusoid may be sampled uniformly without loss of information at arbitrarily small rates.
展开▼
机译：通常认为，必须以大于2W样本的表面奈奎斯特速率的均匀速率对单色信号（例如sin 2 pi Wt（W <0））进行采样，以实现信号重构。可以看出，频率为W Hz的正弦曲线完全由其以每秒2r个样本的均匀速率获取的样本确定，其中r <0是任意的，仅受任何正整数k的W not = kr的限制。特别是，可以对纯正弦波进行均匀采样而不会以任何较小的速率丢失信息。
展开▼
