### Abstract

*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 |
---|---|

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 |

### Fingerprint

### Keywords

- Sampling
- Z-Transform
- Zeta Function

### Cite this

*Open Journal of Discrete Mathematics*,

*1*(2), 62-65. https://doi.org/10.4236/ojdm.2011.12008

}

*Open Journal of Discrete Mathematics*, vol. 1, no. 2, pp. 62-65. https://doi.org/10.4236/ojdm.2011.12008

**Log-time sampling of signals : Zeta transform.** / Olkkonen, Hannu (Corresponding Author); Olkkonen, Juuso T.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Log-time sampling of signals

T2 - Zeta transform

AU - Olkkonen, Hannu

AU - Olkkonen, Juuso T.

PY - 2011

Y1 - 2011

N2 - 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.

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.

KW - Sampling

KW - Z-Transform

KW - Zeta Function

U2 - 10.4236/ojdm.2011.12008

DO - 10.4236/ojdm.2011.12008

M3 - Article

VL - 1

SP - 62

EP - 65

JO - Open Journal of Discrete Mathematics

JF - Open Journal of Discrete Mathematics

SN - 2161-7635

IS - 2

ER -