Computational assessment of Gabor representations

A comparative assessment of the computational complexity of several Gabor transform algorithms is given, with results in the range O(P)² to O(P log₂ P), where P is the number of data points being transformed. Among the results is a novel algorithm of lower complexity than previously known FFT (fast Fourier transform) based methods. The most efficient of the methods, which uses the Zak transform as an operational calculus, performs the Gabor analysis and synthesis transforms with a complexity comparable to that of the FFT