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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...
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:
:<math> f(t) = \frac{1}{2} a_0 + \sum_{n=1}^{\infty}[a_n \cos(\omega_n t) + b_n \sin(\omega_n t)] </math>
where, ''n'' is an integer and
:<math> \omega_n = n\frac{2\pi}{T}</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>
The Fourier series of a function ''f(t)'' is of the form:
:<math> f(t) = \frac{1}{2} a_0 + \sum_{n=1}^{\infty}[a_n \cos(\omega_n t) + b_n \sin(\omega_n t)] </math>
where, ''n'' is an integer and
:<math> \omega_n = n\frac{2\pi}{T}</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>