A Smooth Non-Rectangular Time-Frequency Segmentation of L2(R2)

We present a direct generalization of local trigonometric bases to decompositions of L2(R2) with non-rectangular support. We describe decompositions of L2(R2) into n subspaces supported on approximate equiangular sectors and work out the case n = 3 in detail. For prototypical decompositions, windowed circular harmonics serve as basis functions. The technique applies equally well to decompositions of higher-dimensional space.