Signals and systems/GF Fourier: Difference between revisions

Revision as of 22:14, 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 $x(t)=x(t+T)\,$ for $T\neq 0$ .

Remember that $e^{j\theta }=cos\theta +jsin\theta \,$

The exponential form of the Fourier series is defined as $x(t)=\sum _{n=-\infty }^{\infty }\alpha _{n}e^{{j2\pi nt}/T}\,$

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

	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>		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>