### Abstract

We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a "hyperbolic time-frequency geometry." Based on this geometry, we define and study a new "hyperbolic class" of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 27-30 |

Number of pages | 4 |

ISBN (Electronic) | 0780308050, 9780780308053 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

Event | 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Victoria, Canada Duration: Oct 4 1992 → Oct 6 1992 |

### Publication series

Name | Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
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### Conference

Conference | 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
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Country | Canada |

City | Victoria |

Period | 10/4/92 → 10/6/92 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing

### Cite this

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis*(pp. 27-30). [274241] (Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/TFTSA.1992.274241

**A unified framework for the Bertrand distribution and the Altes distribution : The new hyperbolic class of quadratic time-frequency distributions.** / Papandreou-Suppappola, Antonia; Hlawatsch, F.; Boudreaux-Bartels, G. F.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.*, 274241, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Institute of Electrical and Electronics Engineers Inc., pp. 27-30, 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, Canada, 10/4/92. https://doi.org/10.1109/TFTSA.1992.274241

}

TY - GEN

T1 - A unified framework for the Bertrand distribution and the Altes distribution

T2 - The new hyperbolic class of quadratic time-frequency distributions

AU - Papandreou-Suppappola, Antonia

AU - Hlawatsch, F.

AU - Boudreaux-Bartels, G. F.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a "hyperbolic time-frequency geometry." Based on this geometry, we define and study a new "hyperbolic class" of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.

AB - We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a "hyperbolic time-frequency geometry." Based on this geometry, we define and study a new "hyperbolic class" of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.

UR - http://www.scopus.com/inward/record.url?scp=33747695181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747695181&partnerID=8YFLogxK

U2 - 10.1109/TFTSA.1992.274241

DO - 10.1109/TFTSA.1992.274241

M3 - Conference contribution

AN - SCOPUS:33747695181

T3 - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

SP - 27

EP - 30

BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

PB - Institute of Electrical and Electronics Engineers Inc.

ER -