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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