The Fourier Transforms: Difference between revisions

Revision as of 10:56, 12 October 2007

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

    $ℱ [a * x (t) + b * y (t)] = a * X (f) + b * Y (f)$

    $ℱ [x (t - a)] = X (t) e^{j 2 π f a}$

    $ℱ [x (a * t)] = \frac{1}{a} X (\frac{f}{a})$

Revision as of 10:56, 12 October 2007 view source 172.16.21.19 (talk) →= Shifting the function changes the phase of the spectrum ← Older edit		Revision as of 10:56, 12 October 2007 view source 172.16.21.19 (talk) →Frequency and amplitude are affected when changing spatial scale inversely Newer edit →
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	<math>\mathcal{F}[x(a*t)] = \frac{1}{a}X(\frac{f}{a})</math>		<math>\mathcal{F}[x(a*t)] = \frac{1}{a}X(\frac{f}{a})</math>


	~~frac{x(t) - x(-t)}{2}</math>~~