Question

energy and power of signals.

(a) Plot the signal x(t) = e−tu(t) and determine its energy. What is the power of x(t)?

(b) How does the energy of z(t) = e−∣t∣, −∞ < t < ∞, compare to the energy of z1(t) = e−tu(t)? Carefully plot the two signals.

(c) Consider the signal
y(t) = sign[xi(t)] =  1 xi(t) ≥ 0

−1 xi(t) < 0

for −∞ < t < ∞,i = 1,2. Find the energy and the power of y(t) when (a)x1(t) = cos(2πt) (b)x2(t) = sin(2πt)

Plot y(t) in each case.

4. (d) Given v(t) = cos(t) + cos(2t).

   i. Compute the power of v(t).
   ii. Determine the power of each of the components of v(t), add

   them and compare the result to the power of v(t).

5. (e) Find the power of s(t) = cos(2πt) and of f(t) = s(t)u(t). How do

   they compare?

Answers: (a) Ex = 0.5; (b) Ez = 2Ez1; (c) Py = 1; (d) Pv = 1.

Answer 1