A pair of quadrature mirror filters provides a decomposition of any Hilbert space $H$ as direct sum of orthogonal subspaces by giving a recipe to construct orthonormal bases of the space itself. The resulting subspaces are related to a finite partition of $[0,1)$ by dyadic intervals. It is known that, under some assumptions on the filter coefficients, the partition can consist of an infinite number of dyadic intervals covering $[0,1)$ except for a denumerable set. A major application of this fact is the construction of libraries of wavelet packets orthonormal bases of $\ld$ obtained by Meyer, Coifman and Wickerhauser. We prove that the same result holds if the exceptional set corresponding to the infinite partition has Hausdorff dimension strictly less then $1/2$ , thus extending the range of the possible wavelet packets orthonormal bases.
On the possible wavelet packets orthonormal bases
SALIANI, Sandra
1995-01-01
Abstract
A pair of quadrature mirror filters provides a decomposition of any Hilbert space $H$ as direct sum of orthogonal subspaces by giving a recipe to construct orthonormal bases of the space itself. The resulting subspaces are related to a finite partition of $[0,1)$ by dyadic intervals. It is known that, under some assumptions on the filter coefficients, the partition can consist of an infinite number of dyadic intervals covering $[0,1)$ except for a denumerable set. A major application of this fact is the construction of libraries of wavelet packets orthonormal bases of $\ld$ obtained by Meyer, Coifman and Wickerhauser. We prove that the same result holds if the exceptional set corresponding to the infinite partition has Hausdorff dimension strictly less then $1/2$ , thus extending the range of the possible wavelet packets orthonormal bases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
