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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University