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arXiv · 2605.22193

A simple derivation of the Fourier transform of the Heaviside function

Robert C. Dalang
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Abstract

We give a rigorous derivation of the Fourier transform of the Heaviside function within a framework for tempered distributions that is suitable for undergraduate engineering and mathematics students. The proofs rely on fundamental concepts typically taught in a freshman-level calculus course, including limits, generalized integrals, integration by parts and the Taylor Remainder Theorem. In passing, we examine the Principle Value of $\frac{1}{x}$ and the relationship between its derivative of order $n$ and the Principle Value of $\frac{1}{x^{n+1}}$.

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Robert C. Dalang. 2026-05-21. A simple derivation of the Fourier transform of the Heaviside function. https://arxiv.org/abs/2605.22193

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