$(i) x (t) = Ae^{-αt}u(t), α > 0\ (ii) x[n] = u[n]$

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 04

Year : MAY 2015

$$(i) x(t) = Ae^{-αt} u(t) α > 0$$

This signal is non-periodic and of infinite duration. It can be energy signal.

Therefore calculating its energy

Energy is given by the equation,

$E = ∫\limits_{-∞}^∞|x(t)|2 dt \\ = ∫\limits_0^∞ [A e^{-∝t}]^2 dt\hspace {1cm} \text {Since} \space u(t) = 1 \text {for} …