We propose an approach for approximating a fitness landscape by filtering its frequency components in order to accelerate evolutionary computation (EC) and evaluate the performance of the technique. In addition to the EC individuals, the entire fitness landscape is resampled uniformly. The frequency information for the fitness landscape can then be obtained by applying the discrete Fourier transform (DFT) to the resampled data. Next, we filter to isolate just the major frequency component; thus we obtain a trigonometric function approximating the original fitness landscape after the inverse DFT is applied. The elite is obtained from the approximated function and the EC search accelerated by replacing the worst EC individual with the elite. We use benchmark functions to evaluate some variations of our proposed approach. These variations include the combination of resampling of the global area, local area, in all n-D at once, and in each of n 1-D. The experimental results show that our proposed method is efficient in accelerating most of the benchmark functions.