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, 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 continous, square integrable functions.
