Fourier transformation is a very important tool for signal analysis but also helpful to simplify the solution of differential equations or the calculation of convolution integrals. An important numerical method is the discrete Fourier transformation which can be used for trigonometric interpolation and also as a numerical approximation to the continuous Fourier integral. It can be realized efficiently by Goertzel’s algorithm or the family of fast Fourier transformation methods. For real valued even functions the computationally simpler discrete cosine transformation can be applied. Several computer experiments demonstrate the principles of trigonometric interpolation and nonlinear filtering.