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== Unit Impulse == | == Unit Impulse == | ||
| − | <math> h(t) = u(t-1) ,</math> | + | <math> h(t) = u(t-1) \,</math><br> |
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| + | <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) = \frac{1}{jw_0}</math><br> | ||
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| + | == Repsonse of the CT system == | ||
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| + | <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> | ||
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| + | <math> y(t) = \frac{1}{j4}e^{\frac{2j2\pi t}{6}} - \frac{1}{j4}e^{\frac{-2j2\pi t}{6}} - \frac{2}{5}e^{\frac{2j5\pi t}{6}} -\frac{2}{5}e^{\frac{-2j5\pi t}{6}}</math> | ||
Latest revision as of 18:48, 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} $
Repsonse of the CT system
$ x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\, $
$ y(t) = H(s)x(t)\, $
$ y(t) = \frac{1}{j4}e^{\frac{2j2\pi t}{6}} - \frac{1}{j4}e^{\frac{-2j2\pi t}{6}} - \frac{2}{5}e^{\frac{2j5\pi t}{6}} -\frac{2}{5}e^{\frac{-2j5\pi t}{6}} $
