Signals and systems/GF Fourier: Difference between revisions

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The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines.
The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines.

A function is considered periodic if <math> x(t) = x(t+T)\, </math> for <math> T \neq 0 </math>.
A function is considered periodic if <math> x(t) = x(t+T)\, </math> for <math> T \neq 0 </math>.
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The exponential form of the Fourier series is defined as <math> x(t) = \sum_{n=-\infty}^\infty \alpha_n e^{{j2\pi nt}/T} \, </math>


==Notes==
Remember that <math>e^{j \theta} = cos \theta + j sin \theta \, </math>
<math>e^{j \theta} = cos \theta + j sin \theta \, </math>

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The exponential form of the Fourier series is defined as <math> x(t) = \sum_{n=-\infty}^\infty \alpha_n e^{{j2\pi nt}/T} \, </math>

Revision as of 22:20, 28 October 2006

The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines. A function is considered periodic if for . The exponential form of the Fourier series is defined as

Notes

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