Chapter 2
Signal and Linear System Analysis
2.1
Problem Solutions
Problem 2.1
a. For the single-sided spectra, write the signal as
x1 (t) = 10 cos(4 t + =8) + 6 sin(8 t + 3 =4)
= 10 cos(4 t + =8) + 6 cos(8 t + 3 =4
=2)
= 10 cos(4 t + =8) + 6 cos(8 t + =4)

Chapter 12
Information Theory and Coding
12.1
Problem Solutions
Problem 12.1
The transition probabilities for the 3-hop system are (The first matrix represents the 2-hop
system as defined by equations (12.19)-(12.22)
( |) =
This gives
=
11 12
21 22
1 1 +

Chapter 11
Optimum Receivers and Signal
Space Concepts
Problem 11.1
a. Given H1 , Z = N , so
10z
fZ (zjH1 ) = fN (n) jz=n = 10e
u (z)
Given H2 , Z = S + N , where S and N are independent. Thus, the resulting pdf under
H2 is the convolution of the separate

Chapter 3
Basic Modulation Techniques
3.1
Problems
Problem 3.1
The demodulated output, in general, is
() = Lpcfw_ () 2 cos[ + ()]
where Lp cfw_ denotes the lowpass portion of the argument. With
() = () cos [ + 0 ]
the demodulated output becomes
() = Lp

Chapter 5
Principles of Baseband Digital
Data Transmission
5.1
Problem Solutions
Problem 5.1
a. Split phase or bipolar RZ;
b. NRZ change or NRZ mark;
c. Split phase;
d. NRZ mark;
e. Polar RZ;
f. Unipolar RZ.
Problem 5.2
These are a matter of lling in the

Chapter 8
Noise in Modulation Systems
8.1
Problems
Problem 8.1
Degrees kelvin (degrees absolute) are converted to to the Celsius scale by substracting 273
(actually 273.15). Degrees Celsius are converted to degrees Fahrenheit by the familiar
expression
9

Chapter 10
Advanced Data Communications
Topics
10.1
Problem Solutions
Problem 10.1
Use the relationship
Rb = (log2 M ) Rs bps
where Rb is the data rate, Rs is the symbol rate, and M is the number of possible signals
per signaling interval. In this case, R

Chapter 9
Principles of Digital Data
Transmission in Noise
9.1
Problem Solutions
Problem 9.1
The signal-to-noise ratio is
z=
A2 T
A2
=
N0
N0 R
Trial and error using the asymptotic expression Q (x)
Q-function program in MATLAB) shows that
PE = Q
p
2z = 10

Chapter 6
Overview of Probability and
Random Variables
6.1
Problem Solutions
Problem 6.1
S = sample space is the collection of the 21 parts. Let Ai = event that the pointer stops
on the ith part, i = 1; 2; :; 21. These events are exhaustive and mutually e

Chapter 4
Angle Modulation and
Multiplexing
4.1
Problems
Problem 4.1
By definition
() = cos [ + ()] = cos [ + ( 0 )]
The waveforms are shown below. The the top pane represents the unmodulated signal. The
middle pane is for is for = , and the bottom-right

Chapter 7
Random Signals and Noise
7.1
Problem Solutions
Problem 7.1
The various sample functions are as follows. Sample functions for case (a) are horizontal
lines at levels 2A; 0; 2A, each case of which occurs equally often (with probability 1/3).
Sampl