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|Title:||Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn)|
|Authors:||Packer, J.A. |
Finitely generated projective modules
|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|
|Appears in Collections:||Staff Publications|
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