Progressive orthogonal tilings of the time-frequency plane
Manuel A. Sola, Sebastià Sallent · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
This paper proposes a fast splitting algorithm (FSA) for a signal that when combined with an optimally criterion defined in the frequency domain leads to coherent tilings of the time- frequency plane. For a given set of basis regions formed by allowed subsets of the signal and a cost function defined over this set, we find the minimum cost cover of the signal by means of a fast algorithm. We show how when an additive cost measure is defined over the subband decomposition induced by a given filter bank, the method admits a solution in the form of a progressive orthogonal tiling. When progressive conditions are verified this method can be modelled with simple structures such as trellis diagrams or ordinary Petri nets. The extension of this method to bidimensional signals and conditions for fast algorithms are also discussed. The set of partitions obtained by the double tree algorithm is included in those considered by the FSA, allowing the later better signal analysis. We also present two approaches that reduced properly the complexity of the FSA maintaining the improvements of the method. The first one is based in constraining the set of basis regions to those with dyadic support, while the second one bounds the maximum support of basis regions.