A smooth non-rectangular time-frequency segmentation of L/sup 2/(R/sup 2/)

We present a direct generalization of local trigonometric bases to decompositions of L/sup 2/(R/sup 2/) with non-rectangular support. We describe decompositions of L/sup 2/(R/sup 2/) into n subspaces supported on approximate equiangular sectors and work out the case for 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.

[1]  Jelena Kovacevic,et al.  Image coding with windowed modulated filter banks , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[2]  John Princen,et al.  Frequency scalable video coding using the MDCT , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[3]  G. Weiss,et al.  Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets , 1993 .

[4]  Xiang-Gen Xia,et al.  Construction of Malvar Wavelets on Hexagons , 1996 .

[5]  Riccardo Bernardini,et al.  Local orthogonal bases II: Window design , 1996, Multidimens. Syst. Signal Process..

[6]  Louis Dunn Fielder,et al.  AC-3: Flexible Perceptual Coding for Audio Transmission and Storage , 1994 .

[7]  D. Rockmore,et al.  Nonlinear approximation theory on finite groups , 1999 .

[8]  Dennis M. Healy,et al.  Statistical best bases for fast encoding in magnetic resonance imaging , 1995, Defense, Security, and Sensing.

[9]  X. Xia,et al.  A Family of Two-Dimensional Nonseparable Malvar Wavelets , 1995 .

[10]  M. Liebeck,et al.  Representations and Characters of Groups , 1995 .

[11]  Riccardo Bernardini,et al.  Local orthogonal bases I: Construction , 1996, Multidimens. Syst. Signal Process..