### Abstract

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 orthogonal boundary filters; these allow us to construct essentially arbitrary tilings. We present a double-tree algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g. rate-distortion). This gives best time-varying bases. Results of experiments on test signals are shown.

Original language | English (US) |
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Title of host publication | Digital Speech Processing |

Publisher | Publ by IEEE |

Volume | 3 |

ISBN (Print) | 0780309464 |

State | Published - Jan 1 1993 |

Event | 1993 IEEE International Conference on Acoustics, Speech and Signal Processing - Minneapolis, MN, USA Duration: Apr 27 1993 → Apr 30 1993 |

### Other

Other | 1993 IEEE International Conference on Acoustics, Speech and Signal Processing |
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City | Minneapolis, MN, USA |

Period | 4/27/93 → 4/30/93 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics

### Cite this

*Digital Speech Processing*(Vol. 3). Publ by IEEE.

**Time-varying orthogonal tilings of the time-frequency plane.** / Herley, Cormac; Kovacevic, Jelena; Ramchandran, Kannan; Vetterli, Martin.

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

*Digital Speech Processing.*vol. 3, Publ by IEEE, 1993 IEEE International Conference on Acoustics, Speech and Signal Processing, Minneapolis, MN, USA, 4/27/93.

}

TY - GEN

T1 - Time-varying orthogonal tilings of the time-frequency plane

AU - Herley, Cormac

AU - Kovacevic, Jelena

AU - Ramchandran, Kannan

AU - Vetterli, Martin

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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 orthogonal boundary filters; these allow us to construct essentially arbitrary tilings. We present a double-tree algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g. rate-distortion). This gives best time-varying bases. Results of experiments on test signals are shown.

AB - 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 orthogonal boundary filters; these allow us to construct essentially arbitrary tilings. We present a double-tree algorithm which for a given signal decides on the best binary segmentation, and which tree split to use for each segment. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g. rate-distortion). This gives best time-varying bases. Results of experiments on test signals are shown.

UR - http://www.scopus.com/inward/record.url?scp=0027228785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027228785&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027228785

SN - 0780309464

VL - 3

BT - Digital Speech Processing

PB - Publ by IEEE

ER -