Question

1.35 Determine if each of the following signals is a power signal, an energy signal, or neither (а) х1() — [1 —е 2] u(0) (b) x2(t) 2 sin(4t ) cos(4t) (с) хз(t) — 2 sin(3t) cos(4t)

Answer 1

Finite duration signals, at t rightarrow plusminus infinity, x(t) = 0 those are energy signals rightarrow periodic signals and constant amplitude signals are power signals. (a) x_1(t) = (1 - e^-2t)u(t) so, x_1(t) is neither energy nor power signal (b) x_2(t) = 2 sin (4t) cos (4t) x_2(t) = sin (8t) w_0 = 8 rad/sec rightarrow T = 2pi/8 sec rightarrow x_2(t) is periodic signal with period T = 2pi/8 sec so, x_2(t) is power signal. (c) x_3(t) = 2 sin (3t) cos (4t) x_3(t) = sin(3t + 4t)+ sin(3t - 4t) [Therefore sin(a + b)+ sin(a-b) = 2 sin a cos b] x_3(t) = sin(7t)-sin(t) w_0 = GCD (w_1, w_2) w_0 = 1 rad/sec T = 2pi sec x_3(t) i.e. periodic signal with period T = 2 pi sec so, x_3(t) is power signal. \r\n (a) x_1(t) = e^jat P = Lt_T rightarrow infinity 1/2T integral^T_-T Vertical-bar x_1(t) Vertical-bar ^2 dt P = Lt_T rightarrow infinity 1/2T