Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 05

Year : MAY 2014

We know that, Energy

$= \lim\limits_{T→∞} ∫\limits_{-T}^T |x(t)|^2 dt $ and

Power $= \lim\limits_{T→∞} \dfrac 1{2T}⁡∫\limits_{-T}^T |x(t)|^2 dt,$ so let us first find

$∫\limits_{-T}^T|x(t)|^2 dt \\ ∴ ∫\limits_{-T}^T|x(t)|^2 dt =∫\limits_{-T}^T|(3\cos5Ωt)|^2 dt \\ = ∫\limits_{-T}^T(3\cos5Ωt)^2 dt \\ = ∫\limits_{-T}^T9\cos^2 (5Ωt)dt \\ = 9∫\limits_{-T}^T[\dfrac {1+\cos10Ωt}2]dt = \dfrac 92 ∫\limits_{-T}^T[1+\cos10Ωt]dt = 4.5 [t+ …