Author(s)

Hannu Olkkonen, Juuso T. Olkkonen

.

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 t_n=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 f_n=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.

Sampling, Z-Transform, Zeta Function

H. Olkkonen and J. Olkkonen, "Log-Time Sampling of Signals: Zeta Transform," Open Journal of Discrete Mathematics, Vol. 1 No. 2, 2011, pp. 62-65. doi: 10.4236/ojdm.2011.12008.