Difference between revisions of "Fourier series"

From Conservapedia
Jump to: navigation, search
(New page: 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: :<m...)
 
m
Line 7: Line 7:
 
:<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\omega_n t)\, dt</math> &nbsp; &nbsp;
 
:<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\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;
 
:<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.
 +
 +
[[category: mathematics]]

Revision as of 01:47, 24 March 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 continous, square integrable functions.