The Fourier Transforms: Difference between revisions

Revision as of 20:07, 11 October 2007

The Fourier transform was named after Joseph Fourier, a French mathematician. A Fourier Transform takes a function to its frequency components.

Properties of a Fourier Transform:

@@ Line 7: / Line 7: @@
 ;Convolution
 ::::{|
-|<math>f(t)* g(t) \,</math>
-|&nbsp; &nbsp; <math>\stackrel{\mathcal{F}}{\Longleftrightarrow}\quad
-\sqrt{2\pi}\cdot F(\omega)\cdot G(\omega) \,</math>
-| &nbsp; &nbsp; (unitary convention)
-|-
-|
-|&nbsp; &nbsp; <math>\stackrel{\mathcal{F}}{\Longleftrightarrow}\quad
-F(\omega)\cdot G(\omega) \,</math>
-| &nbsp; &nbsp; (non-unitary convention)
-|-
-|
-|&nbsp; &nbsp; <math>\stackrel{\mathcal{F}}{\Longleftrightarrow}\quad
-F(f)\cdot G(f) \,</math>
-| &nbsp; &nbsp; (ordinary frequency)
-|}