Short-time Fourier analysis-a novel window design procedure

Weyl-Heisenberg frames are the tool for short-time Fourier analysis. These are generated from a prototype window function using translation on a rectangular grid in the time-frequency plane. Particularly appealing Weyl-Heisenberg frames are those which are tight as they allow for signal representations analogous to orthonormal expansions and have good numerical stability properties. Designing the window of a tight Weyl-Heisenberg frame requires optimization of the frequency characteristics of the window, usually some form of frequency selectivity, under a set of nonlinear constraints. For long windows this can be a formidable task, if not infeasible. We propose a new filter design method based on expansions with respect to prolate spheroidal sequences. The advantages of this new method are more and more pronounced as the redundancy of the frame increases. These advantages pertain to a reduction in computational complexity and the ability to describe good and long windows with a few parameters.