A new particle swarm optimization (PSO) algorithm has been developed, and combined with the differential evolution (DE) method. The novel evolutionary technique is utilized to approximate the sine and Gaussian functions of a Gabor filter, as polynomial functions, by the stochastic computation of an optimal set of coefficients. The new stochastic algorithm achieves a lower root mean square error of 0.0185, in comparison to sine and Gaussian approximations using state-machines from another work. Another important feature that adds more value to this work is the fact that polynomial functions can be constructed in hardware, through relatively simply operations, such as shift-add operations.