Abstract: Decomposition and composition of periodic signal is analyzed with trigonometric form of Fourier series in signal and linear systems， and square wave’s decomposition and composition is simulated with Matlab. The experiment result shows that the square wave can be decomposed into the summation of DC component and different frequency cosine components (or sine components). The sum of the DC signal and limited harmonic components under certain conditions can be approximated the square wave. The error and Gibbs phenomenon are analyzed in the process of square wave’s composition. The principle of periodic signal’s decomposition and composition can be comprehended with software simulation, it is very important to understand the concept of the signal spectrum and the system’s spectrum analysis.

Key words: periodic signal, signal’s decomposition and composition, Gibbs phenomenon