| Line 3: | Line 3: | ||
<math> | <math> | ||
y(t) = | y(t) = | ||
| − | \ cos( | + | \ cos(t) |
</math> | </math> | ||
| Line 9: | Line 9: | ||
<math> | <math> | ||
| − | \ cos( | + | \ cos(t) = \sum_{n=0}^\infty \left (-1 \right )^n \frac{t^{2n}}{ \left(2n \right )!} |
</math> | </math> | ||
Revision as of 12:24, 26 September 2008
The function y(t) in this example is the periodic continuous-time signal cos(x) such that
$ y(t) = \ cos(t) $
where cos(x) can be expressed by the Maclaurin series expansion
$ \ cos(t) = \sum_{n=0}^\infty \left (-1 \right )^n \frac{t^{2n}}{ \left(2n \right )!} $
where its Fourier series coefficients are described by the equation
$ \left ( \frac{1}{jk\omega_0} \right )a_k = \left ( \frac{1}{jk \left (2\pi/T \right)} \right )a_k $
