### 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. The method is based on the construction of boundary and transition filters; these allow us to construct essentially arbitrary tilings. Time-varying modulated lapped transforms are a special case, where both boundary and overlapping solutions are possible with filters obtained by modulation. We present a double-tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g., rate-dis-tortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented.

Original language | English (US) |
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Pages (from-to) | 3341-3359 |

Number of pages | 19 |

Journal | IEEE Transactions on Signal Processing |

Volume | 41 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1993 |

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### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering