Log-time sampling of signals: Zeta transform

Hannu Olkkonen (Corresponding Author), Juuso T. Olkkonen

Research output: Contribution to journalArticleScientificpeer-review

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 = 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
Volume1
Issue number2
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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Transform
Nonuniform Sampling
Number theory
Riemann zeta function
Instant
Join
Instantaneous
Linear Combination
Continuous Time
Linearly

Keywords

  • Sampling
  • Z-Transform
  • Zeta Function

Cite this

Olkkonen, Hannu ; Olkkonen, Juuso T. / Log-time sampling of signals : Zeta transform. In: Open Journal of Discrete Mathematics. 2011 ; Vol. 1, No. 2. pp. 62-65.
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Log-time sampling of signals : Zeta transform. / Olkkonen, Hannu (Corresponding Author); Olkkonen, Juuso T.

In: Open Journal of Discrete Mathematics, Vol. 1, No. 2, 2011, p. 62-65.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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KW - Z-Transform

KW - Zeta Function

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