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.