Log-Time Sampling of Signals: Zeta Transform

• 作者: Hannu Olkkonen Juuso T. Olkkonen
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Sampling Z-TRANSFORM ZETA FUNCTION
• 年，卷（期）: 2011,（2）
• 页码范围: 62-65
• 页数: 4页
• 分类号: O1

摘要

We introduce a general framework for the log-time sampling of continuous-time signals. We define the zeta transform based on the log-time sampling scheme, where the signal x(t)is sampled at time instants tn=Tlogn,n=1,2,....The zeta transform of the log-time sampled signals can be described by a linear combination of Riemann zeta function, which firmly joins the log-time sampling process to the number theory. The instantaneous sampling frequency of the log-sampled signal equals fn=n/T,n=1,2,..., i.e. it increases linearly with the sampling number. We describe the properties of the log-sampled signals and discuss several applications in nonuniform sampling schemes.