Revision as of 05:13, 29 October 2006

Fourier series

The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines.

A function is considered periodic if $x (t) = x (t + T)$ for $T \neq 0$ .

The exponential form of the Fourier series is defined as $x (t) = \sum_{n = - \infty}^{\infty} α_{n} e^{j 2 π n t / T}$

$e^{j θ} = c o s θ + j s i n θ$

$⟨ n ∣ m ⟩ = T δ_{n, m}$

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 The exponential form of the Fourier series is defined as <math> x(t) = \sum_{n=-\infty}^\infty \alpha_n e^{{j2\pi nt}/T} \, </math>
+==Changing Basis Functions==
 =Notes=