2.9. Find the normalized power for each signal below that is a power signal and the normalized energy for each signal that is an energy signal. If a signal is neither a power signal nor an energy signal, so designate it. Sketch each signal (a is a positive constant). a. x1(t) 2 cos(4+2π/3). b. x2(t)=eatu(t). c. x3(t)=(-1). d. x4(1)(a²+12)-1/2 = e. xs(t) = e-all f. x6 = e¯ª¹u(t)—e¯ª(t−1)u(t−1). a. Power. Since it is a periodic signal, we obtain -To 1 1 4 cos2 (4nt+2/3) dt = -To To Jo 21+cos (8t+4/3)) dt = 2 W where To 1/2 s is the period. The cosine in the above integral integrates to zero because the interval of integratation is two periods. b. Energy. The energy is -2at E2= = c. Energy. The energy is dt = J dt= = E3= J 20 d. Energy. The energy is E4= lim T-x = lim T-x tan -1 dt -(-)- = lim T-xa² = lim T-xx -T dt (1+(1/α)²) -1 [tan (T/a)-tan (-T/a)] e. Energy. Since it is the sum of 22(t) and s(t), its energy is the sum of the energies of these two signals, or Es = 1/a. f. Energy. The energy is Ee= lim T-x = lim = lim T-x [(t) - e(t − 1)]² dt -et-(-1) (1) (1) + (-1) (-1)] d e-3(-1) dt + -T -dt-e (-1) dt T-1 T-1 = lim e-20 dt-e- - dt + dt x Jo -2at 7 -2nt 7-1 -2at' = lim T-x 20 2a 20 lo 10 lo 1 = - 20 20 2a + = J