Reference no: EM133079177

Question 1: For x(t) = a₁cos(wt + θ₁) + a₂cos(wt + θ₂), show that:

p_x ≠ a₁²/2 + a₂²/2

and find the average power of x(t).

Question 2: If the energy of an energy-type signal x(t) is E_x, find the energy of x (t/a).

Question 3: If the power of a periodic signal x(t) is P_x, find the average power of x (t/a).

Question 4: Determine which of the following systems are (i) LTI, (ii) Memoryless, (iii) Causal, and (iv) Stable:

(a) y(t) = a₁x(t - t1) + a₂x(r - t₂)
(b) Y(t) = e^x(t)
(c) y(t) = x(t)cos(ω_ot)
(d) y[n] - y[n - 1] = x[n] (Hint: represent y(t) as a summation of x[n])
(e) y(t) = 4
(0 Y[n] = lx[n]l

Question 5: Classify the following signals into energy-type signals, power-type signals, and neither energy-type nor power-type signals and calculate the energy and power for each signal:
(a) x₁ = Π(t) + ∧(2t)
(b) x₂[n] = ∧[n/10]
(c) x₃(t) = e-jwt, -∞< t < ∞
(d) x₄(t) = u(t)