Author(s)

Hannu Olkkonen, Juuso T. Olkkonen

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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

Olkkonen, H. and Olkkonen, J. (2011) Log-Time Sampling of Signals: Zeta Transform. Open Journal of Discrete Mathematics, 1, 62-65. doi: 10.4236/ojdm.2011.12008.