| Line 9: | Line 9: | ||
<math>h(t) = 7\delta(t-4) \!</math> | <math>h(t) = 7\delta(t-4) \!</math> | ||
| − | <math>H(s) = 7e^{- | + | <math>H(s) = 7e^{-4s} \!</math> |
===HW 4.1 Response=== | ===HW 4.1 Response=== | ||
| + | |||
| + | HW 4.1 signal | ||
| + | |||
| + | <math>\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t}</math> | ||
| + | |||
| + | The response is equal to | ||
| + | |||
| + | The convolution of the input signal and the system. | ||
| + | |||
| + | <math>7e^{-4jt}\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + 7e^{-4jt}\frac{1}{2}(e^{j3\pi t} + 7e^{-4jt}e^{-j3\pi t}) + e^{j2\pi t}</math> | ||
Revision as of 16:36, 26 September 2008
The CT LTI Signal
$ y(t) = 7x(t-4) \! $
The Unit Impulse Response
$ y(t) = 7x(t-4) \! $
$ h(t) = 7\delta(t-4) \! $
$ H(s) = 7e^{-4s} \! $
HW 4.1 Response
HW 4.1 signal
$ \frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t} $
The response is equal to
The convolution of the input signal and the system.
$ 7e^{-4jt}\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + 7e^{-4jt}\frac{1}{2}(e^{j3\pi t} + 7e^{-4jt}e^{-j3\pi t}) + e^{j2\pi t} $
