Question

Consider the signal: x() 10 cos (30mt ) a) Determine the frequency and the angular frequency of x(t) b) Find the energy of x (t) c) Find the power of x(t). d) Determine whether x(t) is a power or an energy signal.

Answer 1

Given x (t) = 10 cos (30 pi t + pi/3) = -A cos (wt + theta) w = 2 pi f = 30 pi frequency implies f = 15 Hz Angular frequency w = 30 pi rad/s the energy of a signal x (t) is given as E_infinity = integral^infinity_-infinity Vertical-bar x (t) Vertical-bar ^2 dt As given is periodic signal, it is exists from + infinity to -infinity for finding the energy, we are taking the modulus of the signals x (t) i.e Vertical-bar x (t) Vertical-bar , so the entire signal becomes positive over the infinite period the energy of this period signal becomes infinity E = infinity \r\n the power of a signal x (t) is given as P_av = 1/T integral^T/2_-T/2 Vertical-bar x (t) Vertical-bar ^2 dt = (R M S)^2 for given signal R M S value = maximum vale/squareroot 2 = 10/squareroot 2 P_av = (10/squareroot 2)^2 = 100/2 = 50 w All the periodic signals are power signals because the energy is infinity and power is finite