(→unit impulse response) |
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:<math>h(t)=10d(t) +d(t-1)\,</math> | :<math>h(t)=10d(t) +d(t-1)\,</math> | ||
:<math>H(s)=\int_{-\infty}^{\infty} h(t)e^{-s t}dt</math> | :<math>H(s)=\int_{-\infty}^{\infty} h(t)e^{-s t}dt</math> | ||
| + | :<math>H(s)=\int_{-\infty}^{\infty} (10d(t) +d(t-1))e^{-s t}dt</math> | ||
| + | |||
| + | Using the shifting property, | ||
| + | :<math>H(s)= | ||
Revision as of 05:46, 25 September 2008
CT LTI system
The system is:
- $ y(t)=10x(t)+x(t-1) $
unit impulse response
Obtain the unit impulse response h(t) and the system function H(s) of your system. :
- $ d (t) => System =>10 d (t) + d(t-1)\, $
- $ h(t)=10d(t) +d(t-1)\, $
- $ H(s)=\int_{-\infty}^{\infty} h(t)e^{-s t}dt $
- $ H(s)=\int_{-\infty}^{\infty} (10d(t) +d(t-1))e^{-s t}dt $
Using the shifting property,
- $ H(s)= $
