Tilings of the Time-Frequency Plane: Construction of Arbitrary Orthogonal Bases and Fast Tiling Algorithms

Cormac Herley, Jelena Kovacevic

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)3341-3359
Number of pages19
JournalIEEE Transactions on Signal Processing
Issue number12
StatePublished - Dec 1993


ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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