Fourier Series and Transform

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Revision as of 22:58, 5 December 2022 by Ecarder (talk | contribs) (Created page with "A Fourier series is an expansion of trigonometric functions to model periodic functions. This method proves useful in the study of harmonic systems as the analysis in a more familiar domain is much simpler than in its original domain. It has a variety of applications ranging from signal processing to quantum mechanics. The Fourier Series is defined as <math>f(x)=\sum_{n=1}^{\infty}{a_n\cos{(\frac{nx}{L}})}+\sum_{n=1}^{\infty}{b_n\sin{(\frac{nx}{L}})}</math> ==Intuition==...")
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A Fourier series is an expansion of trigonometric functions to model periodic functions. This method proves useful in the study of harmonic systems as the analysis in a more familiar domain is much simpler than in its original domain. It has a variety of applications ranging from signal processing to quantum mechanics. The Fourier Series is defined as [math]\displaystyle{ f(x)=\sum_{n=1}^{\infty}{a_n\cos{(\frac{nx}{L}})}+\sum_{n=1}^{\infty}{b_n\sin{(\frac{nx}{L}})} }[/math]

Intuition

Many physical systems can be modeled by square waves. Consider systems with on-off behavior, similar to an on-and-off switch. A square wave looks like this:

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