The following problems are from both Lathi's Text and other sources.
*1. From the definition of average (dc) value, find the average values of the following signals,
x(t), y(t) and z(t):
x(t)
A sin(\omega t)
A
\frac{A}{t}, \alpha > 0
z(t)
2
t
t
0 \frac{T}{2} T
0
0
2
3
5
7
8
*2. a) Find the energy, $E_x$, of the following signal:
x(t)
4
0
2
4
t
Next, using the definition of energy, find the energy of y(t) = (-c)x(-t-1) in terms of $E_x$.
(Note: assume "c" to be a constant)
b) Compute the energy of the signal, z(t) = \begin{cases} 3e^{-2t-j3t}, & \text{for } t \ge 0\\0 & \text{for } t \le 0 \end{cases}
*3) a) Find the RMS values of the waveforms, x(t) and z(t), shown in Problem 1 above.
b) From the values of $x_{dc}$ and $x_{RMS}$ found above, find the RMS value of $x_1(t) = x(t) - x_{dc}$.
c) Using the known properties of the power of a sum orthogonal signals, find the RMS
values of the following signals:
i) p(t) = 3 - 4cos(20\pi t + \frac{\pi}{3})sin(10t - \frac{\pi}{5})
ii) q(t) = 2 - sin^2(10t)
iii) r(t) = 2e^{-2t}cos(10t) - 3
