6. Conclusion

The problem of computing the two-dimensional Fourier transform is highly illposed. Noise can give rise to large errors if the Fourier series formula is used. The regularized two-dimensional Fourier series is presented. The convergence property is proved and tested by some examples. The convergence property and numerical results show that the regularized two-dimensional Fourier series is excellent in computation in noisy cases. The algorithm will be useful in image processing and multi-dimensional signal processing. The method will be of interest to: engineers who want higher precision in the gauging and design of function generators and analyzers; the electronic or electrical rectification industry; and also to the mathematics community for computing methods and the improvement of mathematics programs on signals and systems, for example, Simulink; and others since many problems in engineering involve noise.
