论文标题
样本序列曲线的周期和信号重构
Period and Signal Reconstruction from the Curve of Sample-Sequences
论文作者
论文摘要
可以在多维空间中使用一个点标识的周期信号的等距样品（样品序列）的有限序列。这样的点取决于采样信号，采样周期和序列的启动时间。如果起始时间有所不同，则相应的点沿着封闭的曲线移动。我们证明这样的曲线，即给定长度的所有样品列车的集合，都决定了采样信号的周期，前提是已知采样周期。即使火车很短，也是如此，并且包括列车的样品以次要速率采用。借助庞加莱（Poincaré）开发的旋转理论证明了结果的结果。我们还证明，如果采样周期与信号周期的比率是不合理的，则样品列的曲线将采样信号确定为时间移动。最终，我们举了一个示例，该示例表明无法删除对周期不可通信的假设。
A finite sequence of equidistant samples (a sample train) of a periodic signal can be identified with a point in a multi-dimensional space. Such a point depends on the sampled signal, the sampling period, and the starting time of the sequence. If the starting time varies, then the corresponding point moves along a closed curve. We prove that such a curve, i.e., the set of all sample trains of a given length, determines the period of the sampled signal, provided that the sampling period is known. This is true even if the trains are short, and if the samples comprising trains are taken at a sub-Nyquist rate. The presented result is proved with a help of the theory of rotation numbers developed by Poincaré. We also prove that the curve of sample trains determines the sampled signal up to a time shift, provided that the ratio of the sampling period to the period of the signal is irrational. Eventually, we give an example which shows that the assumption on incommensurability of the periods cannot be dropped.
