Arbitrary tilings of the time-frequency plane using local bases

We show how to design filters given a prescribed tiling of the time-frequency plane. Moreover, we impose on these filters the structure of local orthogonal bases. These bases were recently constructed as a generalization of the cosine-modulated filter banks in discrete time and local trigonometric bases in continuous time. They have been found to be of considerable practical importance due to their simplicity (all filters are obtained from a single prototype) and low computational complexity. We show examples of design, in particular, that of a critical-band system for use in audio coding.