The Influence of the Fourier Transform Convergence on the Continuous Signals Processing

The Fourier transform is very important in signal processing. The number of important problems of the applied nature is connected with its usage. However, scientists use very often the discrete Fourier transform. Many scientific publications, both foreign and domestic, are devoted to this issue. With the continuous Fourier transform, the situation is the opposite, although it also has considerable applied value. That is why we examine one of the most important aspects of the continuous Fourier transform usage. Namely, we investigate the convergence rate of the continuous Fourier transform. In the course of the conducted research, the dependence between the smoothness of the function describing the signal and the rate of convergence of its continuous Fourier transform has been shown. We have also found that taking into account this dependence can improve the quality of the investigated signal processing.