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A link between the Fourier and Heaviside representations of the square wave. (English) Zbl 0773.42002

Summary: By Laplace transforming the Fourier expansion of the odd periodic extension of the square wave and then taking inverse transforms on the results, 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.

MSC:

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
44A10 Laplace transform
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A30 Linear ordinary differential equations and systems
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