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The Uncertainty Principle
The uncertainty principle (for Fourier transform pairs) follows
immediately from the scaling theorem (§B.4). It may be
loosely stated as
Time Duration
Frequency
Bandwidth
c
where
is some constant determined by the
precise definitions of ``duration'' in the time domain and
``bandwidth'' in the frequency domain.
If duration and bandwidth are defined as the ``nonzero interval,''
then we obtain
, which is not useful. This conclusion
follows immediately from the definition of the Fourier transform
and its inverse (§2.2).
Subsections
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