Stable filtering schemes for rational dilations
Brody Johnson
Abstract:
This work seeks to establish a means for the construction of stable
filtering schemes with rational dilations through the theory of
shift-invariant spaces. In particular, principal shift-invariant spaces
will be shown to offer frame wavelet decompositions for rational dilations
even when the associated scaling function is not refinable. Moreover, such
decompositions give rise to stable filtering schemes with finitely
supported filters, reminiscent of those studied by Kovacevic and
Vetterli.
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