(→Unit Impulse) |
(→Unit Impulse) |
||
| Line 3: | Line 3: | ||
<math> h(t) = u(t-1) \,</math><br> | <math> h(t) = u(t-1) \,</math><br> | ||
| + | |||
<math> H(s) = \int^{\infty}_{-\infty} u(t-1)e^{-jw_0 t} dt\,</math><br> | <math> H(s) = \int^{\infty}_{-\infty} u(t-1)e^{-jw_0 t} dt\,</math><br> | ||
| + | |||
<math> H(s) = \int^{\infty}_{1}e^{-jw_0 t} dt\,</math><br> | <math> H(s) = \int^{\infty}_{1}e^{-jw_0 t} dt\,</math><br> | ||
| − | <math> H(s) = \frac{1}{jw_0} | + | |
| + | <math> H(s) = \frac{1}{jw_0}<br> | ||
| + | |||
| + | |||
| + | == Repsonse of the CT system == | ||
| + | |||
| + | <math> x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\,</math><br> | ||
| + | |||
| + | <math> y(t) = H(s)x(t)\,</math><br> | ||
| + | |||
| + | <math> | ||
Revision as of 18:41, 25 September 2008
Unit Impulse
$ h(t) = u(t-1) \, $
$ H(s) = \int^{\infty}_{-\infty} u(t-1)e^{-jw_0 t} dt\, $
$ H(s) = \int^{\infty}_{1}e^{-jw_0 t} dt\, $
$ H(s) = \frac{1}{jw_0}<br> == Repsonse of the CT system == <math> x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\, $
$ y(t) = H(s)x(t)\, $
