Understanding the Fourier and Laplace transforms through visual interpretation

This paper offers basic knowledge about the Fourier and Laplace transforms shown through graphical interpretation. Mathematical and graphical comparisons between the Fourier and Laplace transforms are presented in general form and also on a specific example. It describes the definition of the both transforms and clarifies the Region of convergence (ROC) of the Laplace transform. Based on these facts, the basic definition formula of the stability of electronic systems is described and explained. Visualizations are shown in the 2D and 3D plots constructed in Matlab environment.