Arbitrary Tilings of the Time-Frequency Plane Using Local Bases

We show how to obtain arbitrary tilings of the time-frequency plane using 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. 

Due to the fact that they use a single prototype window, those bases also lead to time-varying tilings. Moreover, they have a fast implementation algorithm, and allow for multidimensional irreducible basis functions. We show examples of design, in particular, that of a critical-band system for use in audio coding.