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)=10 e^{0 s} + e^{-1 s} \, $
- $ H(s)=10 + e^{- s} \, $
