Determine the values of P x and Ex for each of the following signals: (a) x 1 (t) = e- 21 u(t)
x1(t)=e−2tu(t)x_1(t)=e^{-2t}u(t)x1(t)=e−2tu(t)
t=∞ ⟹ x1(t)=0 ⟹ t=\infin \implies x_1(t)=0 \impliest=∞⟹x1(t)=0⟹ It is energy signal
Therefore, Power , Px=0
Energy , Ex=limt→∞∫0t(e−2t)2dt=limt→∞e−ut−u∣0t=14JEx=\lim\limits_{t\to \infin} \int_0^t(e^{-2t})^2dt=\lim\limits_{t\to \infin} \frac{e^{-ut}}{-u}|_0^t=\frac{1}{4}JEx=t→∞lim∫0t(e−2t)2dt=t→∞lim−ue−ut∣0t=41J
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