Question

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

          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

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(ωt)
A
(A)/(t), α> 0
z(t)
2
t
t
0 (T)/(2) T
0
0
2
3
5
7
8
*2. a) Find the energy, Ex, 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 Ex.
(Note: assume "c" to be a constant)
b) Compute the energy of the signal, z(t) = 3e^-2t-j3t, for t ≥0
0 for t ≤0
*3) a) Find the RMS values of the waveforms, x(t) and z(t), shown in Problem 1 above.
b) From the values of xdc and xRMS found above, find the RMS value of x1(t) = x(t) - xdc.
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(20πt + (π)/(3))sin(10t - (π)/(5))
ii) q(t) = 2 - sin^2(10t)
iii) r(t) = 2e^-2tcos(10t) - 3

Added by Tammy R.

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