| Line 4: | Line 4: | ||
Frequency Response: | Frequency Response: | ||
| + | |||
| + | <math>x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\,</math> | ||
| + | |||
| + | then y(t)=\sum^{\infty}_{k = -\infty}a_k*(h(t)*e^{jj\omega_0 t}) | ||
<math>H(s) = \int^{\infty}_{-\infty} h(\tao)e^{-j\omega_0 r} d\tao</math> by definition | <math>H(s) = \int^{\infty}_{-\infty} h(\tao)e^{-j\omega_0 r} d\tao</math> by definition | ||
Revision as of 11:25, 25 September 2008
LTI System: $ y(t) = Kx(t)\, $ where K is a constant
Unit Impulse Response: $ h(t) = K \delta(t)\, $
Frequency Response:
$ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $
then y(t)=\sum^{\infty}_{k = -\infty}a_k*(h(t)*e^{jj\omega_0 t})
$ H(s) = \int^{\infty}_{-\infty} h(\tao)e^{-j\omega_0 r} d\tao $ by definition
