A link between the Fourier and Heaviside representations of the square wave

Abstract

By Laplace transforming the Fourier expansion of the odd periodic extension of the square wave and then taking inverse transforms on the result, we arrive at a representation of this periodic function as an infinite combination of delayed step functions. This helps to clarify the connection between solutions obtained for constant coefficient linear differential equations with periodic step forcing functions, when using, on the one hand, the Fourier Series approach and on the other, the Laplace transform [1], [2].