| Line 7: | Line 7: | ||
<math>x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\,</math> | <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}) | + | then <math>y(t)=\sum^{\infty}_{k = -\infty}a_k*(h(t)*e^{jj\omega_0 t})</math> |
| − | <math>H(s) = \int^{\infty}_{-\infty} h( | + | <math>H(s) = \int^{\infty}_{-\infty} h(t)e^{-j\omega_0 r} dt</math> by definition |
Revision as of 12:25, 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(t)e^{-j\omega_0 r} dt $ by definition
