# Difference between revisions of "Fourier series"

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(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...) |
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:<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\omega_n t)\, dt</math> | :<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\omega_n t)\, dt</math> | ||

:<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math> | :<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math> | ||

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+ | Fourier series can be generalized to [[Fourier transformation]]s for non-perodic, piecewise continous, [[square integrable function]]s. | ||

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+ | [[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.