Wavelet Filter Functions, the Matrix Completion Problem, and Projective Modules Over C(T n )
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We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective C(T n )-modules. Conversely, we show how cancellation properties for finitely generated projective modules over C(T n ) 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.
KeywordsSignal Processing Pass Filter High Pass Filter High Pass Projective Module
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