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Suppose we have a LTI CT signal y(t)=2x(t)

Unit Impulse Response h(t) and System Function H(s)

$ y(t)=2x(t)=>h(t)=2\delta(t) $

$ H(j\omega)=\int_{-\infty}^\infty h(\tau)e^{-j\omega\tau}d\tau $

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