### 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*t*=_{n}*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*ƒ*=1,2,...,_{n}= n/T, n*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 language | English |
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Pages (from-to) | 62-65 |

Journal | Open Journal of Discrete Mathematics |

Volume | 1 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

MoE publication type | A1 Journal article-refereed |

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### Keywords

- Sampling
- Z-Transform
- Zeta Function

### Cite this

Olkkonen, H., & Olkkonen, J. T. (2011). Log-time sampling of signals: Zeta transform.

*Open Journal of Discrete Mathematics*,*1*(2), 62-65. https://doi.org/10.4236/ojdm.2011.12008