Differentiation Theorem Dual
Theorem: Let
denote a signal with Fourier transform
, and let
(B.6) |
denote the derivative of with respect to . Then we have
(B.7) |
where denotes the Fourier transform of .
Proof:
We can show this by direct differentiation of the definition of the
Fourier transform:
An alternate method of proof is given in §2.3.13.
The transform-pair may be alternately stated as follows:
(B.8) |
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Differentiation Theorem