Scalable filter banks

Youngmi Hur, Kasso A. Okoudjou

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

Abstract

A finite frame is said to be scalable if its vectors can be rescaled so that the resulting set of vectors is a tight frame. The theory of scalable frame has been extended to the setting of Laplacian pyramids which are based on (rectangular) paraunitary matrices whose column vectors are Laurent polynomial vectors. This is equivalent to scaling the polyphase matrices of the associated filter banks. Consequently, tight wavelet frames can be constructed by appropriately scaling the columns of these paraunitary matrices by diagonal matrices whose diagonal entries are square magnitude of Laurent polynomials. In this paper we present examples of tight wavelet frames constructed in this manner and discuss some of their properties in comparison to the (non tight) wavelet frames they arise from.

Original languageEnglish
Title of host publicationWavelets and Sparsity XVI
PublisherSPIE
Volume9597
ISBN (Electronic)9781628417630, 9781628417630
DOIs
Publication statusPublished - 2015 Jan 1
EventWavelets and Sparsity XVI - San Diego, United States
Duration: 2015 Aug 102015 Aug 12

Other

OtherWavelets and Sparsity XVI
CountryUnited States
CitySan Diego
Period15/8/1015/8/12

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Hur, Y., & Okoudjou, K. A. (2015). Scalable filter banks. In Wavelets and Sparsity XVI (Vol. 9597). [95970Q] SPIE. https://doi.org/10.1117/12.2186168