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 exe cution 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 fou nd that convergence did depend on basis choice. The matrix method requ ires a separable Gabor basis (i.e., one that can be generated by takin g a Cartesian product of one-dimensional functions), but is faster tha n the relaxation network by several orders of magnitude. It proved to be a stable and highly accurate algorithm. The Zak-Gabor algorithm req uires that all of the Gabor basis functions have exactly the same enve lope and gives no freedom in choosing the modulating function. Its exe cution, however, is very stable, accurate, and by far the most rapid o f the three methods tested. (C) 1997 Academic Press.