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Differentiation Theorem
Let
denote a function differentiable for all
such that
and the Fourier transforms (FT) of both
and
exist, where
denotes the time derivative
of
. Then we have

(B.4) 
where
denotes the Fourier transform of
. In
operator notation:

(B.5) 
Proof:
This follows immediately from integration by parts:
since
.
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