### Existence of the Fourier Transform

Conditions for the *existence* of the Fourier transform are
complicated to state in general [12], but it is *sufficient*
for to be *absolutely integrable*, *i.e.*,

*square integrable*,

*i.e.*,

There is never a question of existence, of course, for Fourier
transforms of real-world signals encountered in practice. However,
*idealized* signals, such as sinusoids that go on forever in
time, do pose normalization difficulties. In practical engineering
analysis, these difficulties are resolved using Dirac's ``generalized
functions'' such as the *impulse* (also called the
*delta function*) [38].

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The Continuous-Time Impulse

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Number Theoretic Transform