Time-varying orthogonal tilings of the time-frequency plane

Cormac Herley, Jelena Kovacevic, Kannan Ramchandran, Martin Vetterli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationDigital Speech Processing
PublisherPubl by IEEE
Volume3
ISBN (Print)0780309464
StatePublished - Jan 1 1993
Event1993 IEEE International Conference on Acoustics, Speech and Signal Processing - Minneapolis, MN, USA
Duration: Apr 27 1993Apr 30 1993

Other

Other1993 IEEE International Conference on Acoustics, Speech and Signal Processing
CityMinneapolis, MN, USA
Period4/27/934/30/93

Fingerprint

Cost functions
Wavelet transforms
Fourier transforms
Experiments
orthogonality
wavelet analysis
costs
filters
optimization
expansion

ASJC Scopus subject areas

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

Cite this

Herley, C., Kovacevic, J., Ramchandran, K., & Vetterli, M. (1993). Time-varying orthogonal tilings of the time-frequency plane. In 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.

Digital Speech Processing. Vol. 3 Publ by IEEE, 1993.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Herley, C, Kovacevic, J, Ramchandran, K & Vetterli, M 1993, Time-varying orthogonal tilings of the time-frequency plane. in Digital Speech Processing. vol. 3, Publ by IEEE, 1993 IEEE International Conference on Acoustics, Speech and Signal Processing, Minneapolis, MN, USA, 4/27/93.
Herley C, Kovacevic J, Ramchandran K, Vetterli M. Time-varying orthogonal tilings of the time-frequency plane. In Digital Speech Processing. Vol. 3. Publ by IEEE. 1993
Herley, Cormac ; Kovacevic, Jelena ; Ramchandran, Kannan ; Vetterli, Martin. / Time-varying orthogonal tilings of the time-frequency plane. Digital Speech Processing. Vol. 3 Publ by IEEE, 1993.
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