An adaptive filter that enables coefficient computation of the Gabor expansion while employing the least mean-squared algorithm for complex signals is described. A significant simplification of the filter structure and the use of FFT algorithms contribute to a fast and efficient determination of the coefficients when compared with known algorithms for Gabor computation. Based on these results, we propose a hardware realisation using a CORDIC processor. Computer simulations indicate that sufficient precision and a fast convergence of the coefficients can be obtained.