On the uniform sampling of a sinusoidal signal

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.<
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