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**vincisonfire** 1) The basis functions are nonzero for arbitrarily large times. For example, $\displaystyle \sin \left( {(4n+1)\pi\over 2}\right) = 1 $ for arbitrarily large $\displaystyle n\in\mathbb N$.

2) The delta distribution is nonzero for artitrarily large frequencies. Note that $\displaystyle \delta(t) = \int d\omega e^{i\omega t}$, and hence in the freqency domain, $\displaystyle \delta(t)$ is the constant function 1 which does not have compact support (take nonzero values over an infinite range).