THE ORDER OF COMPUTATION FOR FINITE DISCRETE GABOR TRANSFORMS

Equations for the continuous-parameter Gabor transform are presented and converted to finite discrete form suitable for digital computation. A comparative assessment of the computational complexity of several algorithms that execute the finite discrete equations is given, with results in the range O(p2) to O(p log2 p), where P is the number of input data points being transformed. The most efficient of the reviewed methods, which uses the Zak transform as an operational calculus, performs Gabor analysis and synthesis transforms with complexity of the same order as a fast Fourier transform (FFT).