  We discuss how one can use certain filters from signal processing to describe
isomorphisms between certain projective $C(\mathbb T^n)$-modules. Conversely,
we show how cancellation properties for finitely generated projective modules
over $C(\mathbb T^n)$ 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.
