Even-Odd Decomposition Property

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date: 2026-05-21

Any Function can be uniquely decomposed into the sum of an Even Function and an Odd Function

$$\begin{array}{rl}x(t)& =\mathbb{O}(t)+\mathbb{E}(t)\\ & =\frac{x(t)+x(-t)}{2}+\frac{x(t)-x(-t)}{2}\\ & =\frac{x(t)+x(-t)+x(t)-x(-t)}{2}\\ & =\frac{2x(t)}{2}\\ & =x(t)\end{array}$$