Approximate Duals of Gabor-like Frames Based on Realizable Multi-Window Spline-Type Constructions.

Abstract

In the multi-window spline-type spaces, the fast computation of the realizable dual frame could be achieved through a constructive reformulation of the biorthogonal relations. In this paper, we extend the results obtained in spline-type spaces, for the constructive realization of an approximate dual Gabor-like frame. We demonstrate the advantages of this approach in both flexibility and speed. The method allows in a natural way to handle non standard Gabor constructions like non-uniformity in frequency and the reductions of the number of used modulations. Experimental tests are presented in support of the algorithm.