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The Uncertainty Principle
The uncertainty principle (for Fourier transform pairs) follows
immediately from the scaling theorem. 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 very useful. This conclusion
follows immediately from the definition of the Fourier transform
and its inverse in §B.2.
Subsections
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