### Abstract

In this paper we consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. We show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. One method is based on lapped orthogonal transforms, which makes it possible to change the number of channels in the transform. A second method is based on the construction of boundary filters, and gives arbitrary tilings. We present an algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment, and is optimal in a ratedistortion sense. We present the results of experiments on test signals.

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 | 11-14 |

Number of pages | 4 |

ISBN (Electronic) | 0780308050, 9780780308053 |

DOIs | |

State | Published - Jan 1 1992 |

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. 11-14). [274244] (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.1992.274244

**Arbitrary orthogonal tilings of the time-frequency plane.** / Herley, C.; Kovacevic, Jelena; Ramchandran, K.; Vetterli, M.

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

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.*, 274244, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Institute of Electrical and Electronics Engineers Inc., pp. 11-14, 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, Canada, 10/4/92. https://doi.org/10.1109/TFTSA.1992.274244

}

TY - GEN

T1 - Arbitrary orthogonal tilings of the time-frequency plane

AU - Herley, C.

AU - Kovacevic, Jelena

AU - Ramchandran, K.

AU - Vetterli, M.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - In this paper we consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. We show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. One method is based on lapped orthogonal transforms, which makes it possible to change the number of channels in the transform. A second method is based on the construction of boundary filters, and gives arbitrary tilings. We present an algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment, and is optimal in a ratedistortion sense. We present the results of experiments on test signals.

AB - In this paper we consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. We show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. One method is based on lapped orthogonal transforms, which makes it possible to change the number of channels in the transform. A second method is based on the construction of boundary filters, and gives arbitrary tilings. We present an algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment, and is optimal in a ratedistortion sense. We present the results of experiments on test signals.

UR - http://www.scopus.com/inward/record.url?scp=85027663119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027663119&partnerID=8YFLogxK

U2 - 10.1109/TFTSA.1992.274244

DO - 10.1109/TFTSA.1992.274244

M3 - Conference contribution

AN - SCOPUS:85027663119

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

SP - 11

EP - 14

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

PB - Institute of Electrical and Electronics Engineers Inc.

ER -