Difference between revisions of "Fourier series"

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:<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math> &nbsp; &nbsp;
 
:<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math> &nbsp; &nbsp;
  
Fourier series can be generalized to [[Fourier transformation]]s for non-perodic, piecewise continous, [[square integrable function]]s.
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Fourier series can be generalized to [[Fourier transformation]]s for non-perodic, piecewise continuous, [[square integrable function]]s.
  
 
[[category: mathematics]]
 
[[category: mathematics]]

Revision as of 02:00, March 24, 2007

Fourier series express a piecewise continous, periodic function as a linear combination of Sine and Cosine functions.

The Fourier series of a function f(t) is of the form:

where, n is an integer and

   
   
   

Fourier series can be generalized to Fourier transformations for non-perodic, piecewise continuous, square integrable functions.