Suppose we have a LTI CT signal y(t)=2x(t)
Unit Impulse Response h(t) and System Function H(s)
i) $ y(t)=2x(t)=> h(t)=2\delta(t) $
ii) $ H(s)=\int_{-\infty}^\infty h(\tau)e^{-j\omega\tau}d\tau $ $ =\int_{-\infty}^\infty h(\tau)e^{-s\tau}d\tau $
Suppose we have a LTI CT signal y(t)=2x(t)
i) $ y(t)=2x(t)=> h(t)=2\delta(t) $
ii) $ H(s)=\int_{-\infty}^\infty h(\tau)e^{-j\omega\tau}d\tau $ $ =\int_{-\infty}^\infty h(\tau)e^{-s\tau}d\tau $