Question

2. Determine the suitable measures for the following signals (ie energy or power signal) 28) 2e-12 -1 0 g(r)

Answer 1

1st signal is energy signal because it is not a periodic & as t rightarrow infinity, magnitude is decreasing Therefore P_aug = 0 E_infinity = lim_T rightarrow infinity integral^T_-T (x (t))^2 dt = integral^0_-1 (2)^2 dt + integral^infinity_0 (2e^-2t)^2 dt = 4 (t)^0_-1 + 4 integral^infinity_0 e^-4t dt = 4 (0 + 1) + (e^-4t/-4)^infinity_0 = 4 + 4 (e^-infinity - e^0/-4) = 4 + 1 E_infinity = 5 2nd signal is power signal because it is periodic signal therefore E_infinity = infinity P_ aug = 1/T_0 integral^T_0/2_-T_0/2 Vertical-bar g(t) Vertical-bar ^2 dt = 1/2 integral^1_-1 (t + 2)^2 dt = 1/2 integral^1_-1 (t + 2)^2 dt = 1/2 [integral^1_-1 (t^2/2 + 4 + 4t) dt = 1/2 [t^3/3 + 4t + 4t^2/2]^1_-1 = 1/2 [1/3 + 4 + 4/2 - [-1/3 - 4 + 4/2]] = 1/2 [1/3 + 4 + 2 + 1/3 + 4 - 2] = 26/6 p_auy = 13/3 = 4.333

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