The Fourier Transforms: Difference between revisions

Revision as of 19:53, 11 October 2007

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

${\mathcal {F}}[a*x(t)+b*y(t)]={\frac {4}{\pi }}\sum _{k=1}^{\infty }{\sin {\left((2k-1)2\pi ft\right)} \over (2k-1)}$

Revision as of 19:52, 11 October 2007 (view source) 172.20.18.233 (talk) (→‎Linearity) ← Older edit		Revision as of 19:53, 11 October 2007 (view source) 172.20.18.233 (talk) (→‎Linearity) Newer edit →
Line 7:		Line 7:
	==== Linearity ====		==== Linearity ====

	<math>\mathcal{F}[a*X(t)~~]x_{\mathrm{t}}~~(t) = \frac{4}{\pi} \sum_{k=1}^\infty {\sin{\left ((2k-1)2\pi ft \right )}\over(2k-1)}</math>		<math>\mathcal{F}[ax(t) + by(t)] = \frac{4}{\pi} \sum_{k=1}^\infty {\sin{\left ((2k-1)2\pi ft \right )}\over(2k-1)}</math>