(→HW 4.1 Response) |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 17: | Line 17: | ||
<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> | <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 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} +e^{-j3\pi t}) + 7e^{-4jt}e^{j2\pi t}</math> | |
| − | + | ||
| − | <math>7e^{-4jt}\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + 7e^{-4jt}\frac{1}{2}(e^{j3\pi t} + | + | |
Latest revision as of 17:36, 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} +e^{-j3\pi t}) + 7e^{-4jt}e^{j2\pi t} $
