Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00041-003-0010-4
Title: Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn)
Authors: Packer, J.A. 
Rieffel, M.A.
Keywords: C*-algebras
Filters
Finitely generated projective modules
Hubert C*-module
K -theory
Wavelets
Issue Date: 2003
Source: Packer, J.A., Rieffel, M.A. (2003). Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn). Journal of Fourier Analysis and Applications 9 (2) : 101-116. ScholarBank@NUS Repository. https://doi.org/10.1007/s00041-003-0010-4
Abstract: We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective C(double-struck T signn)-modules. Conversely, we show how cancellation properties for finitely generated projective modules over C(double-struck T signn) can often be used to prove the existence of continuous high pass filters, of the kind needed for multivariate wavelets, corresponding to a given continuous low-pass filter. However, we also give an example of a continuous low-pass filter for which it is impossible to find corresponding continuous high-pass filters. In this way we give another approach to the solution of the matrix completion problem for filters of the kind arising in wavelet theory.
Source Title: Journal of Fourier Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/104705
ISSN: 10695869
DOI: 10.1007/s00041-003-0010-4
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