2012 Fall: The Final Exam
1. (Chapter 11)
(a) (6%) There are two kinds of convolutions in literature:
(
P 1
linear convolution
xk ? Ik = Pn=0
xn Ikn
PP 1
P 1
N -point circular convolution xk Ik = n=0 xn mod N I(kn)mod N = Pn=0
xn I(kn)mod N
where cfw_xn

2012 Fall: The Final Exam
1. (Chapter 11)
(a) (6%) There are two kinds of convolutions in literature:
(
P 1
linear convolution
xk ? Ik = Pn=0
xn Ikn
PP 1
P 1
N -point circular convolution xk Ik = n=0 xn mod N I(kn)mod N = Pn=0
xn I(kn)mod N
where cfw_xn

2012 Fall: The Second Midterm of Digital Communications
1. (Chapter 5)
(a) (8%) For a system defined by
r` (t) = s` (t; ) + n` (t),
where s` (t; ) = e s` (t), and n` (t) is additive Gaussian white with two-sided power spectrum density `2 , the likelihood

2012 Fall: The Second Midterm of Digital Communications
1. (Chapter 5)
(a) (8%) For a system defined by
r` (t) = s` (t; ) + n` (t),
where s` (t; ) = e s` (t), and n` (t) is additive Gaussian white with two-sided power spectrum density `2 , the likelihood

2012 Fall: The First Midterm of Digital Communications
1. (Chapter 2)
(a) (5%) Is the system with input x(t), output y(t) and input-output relation
y(t) = Re x(t)e2f0 t
a linear system? If the answer is positive, prove it. If negative, give a counterexa

2012 Fall: The First Midterm of Digital Communications
1. (Chapter 2)
(a) (5%) Is the system with input x(t), output y(t) and input-output relation
y(t) = Re x(t)e2f0 t
a linear system? If the answer is positive, prove it. If negative, give a counterexa