A performance analysis of fast Gabor transform methods

Computation of the finite discrete Gabor transform can be accomplished in a variety of ways. Three representative methods (matrix inversion, Zak transform, and relaxation network) were evaluated in terms of execution speed, accuracy, and stability. The relaxation network was the slowest method tested. Its strength lies in the fact that it makes no explicit assumptions about the basis functions; in practice it was found that convergence did depend on basis choice. The matrix method requires a separable Gabor basis (i.e., one that can be generated by taking a Cartesian product of one-dimensional functions), but is faster than the relaxation network by several orders of magnitude. It proved to be a stable and highly accurate algorithm. The Zak–Gabor algorithm requires that all of the Gabor basis functions have exactly the same envelope and gives no freedom in choosing the modulating function. Its execution, however, is very stable, accurate, and by far the most rapid of the three methods tested.