Log-time sampling of signals: Zeta transform

Hannu Olkkonen (Corresponding Author), Juuso T. Olkkonen

Research output: Contribution to journalArticleScientificpeer-review


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 = T log n, 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 ƒn = 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.
Original languageEnglish
Pages (from-to)62-65
JournalOpen Journal of Discrete Mathematics
Issue number2
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed


  • Sampling
  • Z-Transform
  • Zeta Function

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