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Fourier Transform (FT) and
Inverse
The Fourier transform of a signal
,
, is defined as

(3.4) 
and its inverse is given by

(3.5) 
Thus, the Fourier transform is defined for continuous time and
continuous frequency, both unbounded. As a result, mathematical
questions such as existence and invertibility are most difficult for
this case. In fact, such questions fueled decades of confusion in the
history of harmonic analysis (see Appendix G).
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