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>.
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>


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

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 x(t)=x(t+T) for T≠0. The exponential form of the Fourier series is defined as x(t)=∑n=−∞∞αnej2πnt/T

Notes

ejθ=cosθ+jsinθ

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