TITLE:
Log-Time Sampling of Signals: Zeta Transform
AUTHORS:
Hannu Olkkonen, Juuso T. Olkkonen
KEYWORDS:
Sampling, Z-Transform, Zeta Function
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.2,
July
5,
2011
ABSTRACT: 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.