试论非均匀取样周期信号的数字频谱

On the Digital Spectra of Nonuniformly Sampled Periodic Signal

在许多高速数据采集系统中,由于取样时基抖动等因素影响,取样过程实际上是非均匀的。本文首先介绍这类非均匀取样模型及数字频谱分析的一般原理,然后详细地导出了非均匀取样周期信号的数字频谱表达式,讨论了它们的一些重要特性;最后分析了四种典型的非均匀取样现象,得出了估计非均匀取样周期信号信噪比(S/N)的一般公式及若干结论。本文的思想和有关结论对开展非均匀时间序列分析、谱估计理论研究及高速数据采集系统的设计都有明显价值。

In practice, nonuniform sampling occurs in high speed data acquisition system due to imperfect sampling timebase. In this paper, we first present a mode of nonuniformly sampled signals and basic principle of digital spectrum analysis, and then derive in detail digital spectra representation of nonuniformly sampled periodic signal. Some important properties are explored. Finally, four special but interesting sampling cases are discussed and the signal-to-noise ratio, S/N, is derived in closed form. Several significant conclusions are drawn. The thought and conclusion in this paper are useful for analysing nonuniform time sequence, investigating spectrum estimation and designing high speed data acquisition system.