TEST BANK FOR Fundamentals of Digital Signal Processing Using MATLAB 2nd Ed By Robert J. Schilling
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1.1 Suppose the input to an amplifier is xa(t) = sin(2F0t) and the steady-state output is
ya(t) = 100 sin(2F0t + 1) − 2 sin(4F0t + 2) + cos(6F0t + 3)
(a) Is the amplifier a linear system or is it a nonlinear system?
(b) What is the gain of the amplifier?
(c) Find the average power of the output signal.
(d) What is the total harmonic distortion of the amplifier?
Solution
(a) The amplifier is nonlinear because the steady-state output contains harmonics.
(b) From (1.1.2), the amplifier gain is K = 100.
(c) From (1.2.4), the output power is
Py =
d2
0
4
+
1
2 d2
1 + d+22 + d2
3
= .5(1002 + 22 + 1)
= 5002.5
(d) From (1.2.5)
THD =
100(Py − d2
1/2)
Py
=
100(5002.5− 5000)
5002.5
= .05%
1
p 1.2 Consider the following signum function that returns the sign of its argument.
sgn(t)
=
8<:
1 , t > 0
0 , t = 0
−1 , t < 0
(a) Using Appendix 1, find the magnitude spectrum
(b) Find the phase spectrum
Solution
(a) From Table A2 in Appendix 1
Xa(f) =
1
jf
Thus the magnitude spectrum is
Aa(f) = |Xa(f)|
=
1
|jf|
=
1
|f|
(b) The phase spectrum is
a(f) = 6 Xa(f)
= −6 jf
= −sgn(f)
2
1.3 Parseval’s identity states that a signal and its spectrum are related in the following way.
Z 1
−1 |xa(t)|2dt = Z 1
−1 |Xa(f)|2df
Use Parseval’s identity to compute the following integral.
J = Z 1
−1
sinc2(2Bt)dt
Solution
From Table A2 in Appendix 1 if
xa(t) = sinc(2Bt)
then
Xa(f) =
μa(f + B) − μa(f − B)
2B
Thus by Parseval’s identity
J = Z 1
−1
sin2(2Bt)dt
= Z 1
−1 |xa(t)|2dt
= Z 1
−1 |Xa(f)|2df
=
1
2B Z B
−B
df
= 1
3
1.4 Consider
[Solved] TEST BANK FOR Fundamentals of Digital Signal Processing Using MATLAB 2nd Ed By Robert J. Schilling
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