signals and systems (power and energy signals) Q) Prove that the power of an energy signal is zero over infinite time. Also, prove that the energy of a power signal is infinite over infinite time.
Classify the following signals whether are energy signals, power signals or neither by computing their energy and power: 2. a. (10 points) x1(t)=2cos(2n10t)+3cos(2n20t) 1 < t otherwise (10 points) the periodic signal x3 (t) as shown by the figure below: t + 2 3 b, (10 points) X2(t) = c. x3 (t) 2 -2-1 0 2 3 t(s)
3. (45 pts) On signal energy and power. From the following signals, identify energy signals and power signals. For energy signals, calculate their energy. For power signals, calculate their average signal power. (g) x(t)= rect(t)) (h) x(t) =Loo rect(A) (i) 2(t)=e(-1-j80%(t) (k) x(t) = e-M/2 (l) x[n] = e-jm/2
Instruction: Determine whether the following signals are energy, power, or neither energy nor power. 1. x[n] = (−0.5)n u[n] 2. x[n] = u[n] 3. x[n] = 2ej3n
Determine whether the following signals are power to energy signals or neither. a.) y(t) = r(t) = tu(t) (ramp) b.) z(t) = delta(t) (triangular pulse)
Problem 2. Determine whether the following signals are power or energy signals, or neither. Justify your answers. a) x(t)-Asint -00<t<oo b) x(t) = r(1)-r(1-1) c) x(t)-tu(t) d) x(t)- Aexp(bt) , b>0
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) 1.39 Compute the average power of the following signals (a) x eat for real-valued a (3 j4)e7 (b) х2(г) _ * (с) с х3(t) — eјЗejSi
Calculate the convolution integral of the following signals. Find the energy and power of the input and output signals. x(t) y(t) x(t) = cos(it)[u(t + 1) – uſt – 3)] h(t) = u(t + 2) – uſt – 1) del mes h(t) de ser LTI System
Problem 3. (15 points) Topic: Power and Energy of discrete signals. Find the power of the periodic discrete signal presented below. Answer: P= -10-9-8-7-6-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 1
Find the power or energy of the following signals. xt=0 for t<0(e-t-e-10t) for 0 ≤ t<2 (1-e-5)e-t for t≥2 (16 points) xt=6+5cos30t+3cos60t (8 points)