A fast, discrete Gabor transform via a partition of unity

A partition of unity on the d-dimensional integer lattice Z is used to create a generalized discrete Gabor transform, with analysis and synthesis windows of smooth, desirable characteristics. Factorizing the partition of unity allows for different choices of analysis and synthesis windows, a transformation on general lattices in the time and frequence domains is considered, and an approximate partition of unity via Gaussians gives an approximate inverse. Speed, implementation issues, and practical choices for partitions of unity useful in applications are discussed.