1
Tutorial 5
Random Signal Analysis
Principles of Communications
2
Problem 1
A random process is defined by X (t) = Acos(2 f0t + ) where
is a random variable uniformly distributed on (0, 2). Determine
the mean X (t) and the autocorrelation function RX (t

1
Tutorial 4
Frequency Modulation (FM)
Principles of Communications
2
Problem 1
Consider the following FM signal:
sFM (t) = 100cos(2 ( f ct + sin( f mt) + 2sin(2 f mt)
where fc = 100 kHz and fm=1 kHz. Determine:
(i) Instantaneous phase;
(ii) Instantaneous

1
Tutorial 3
Amplitude Modulation (AM)
Principles of Communications
2
Problem 1 (AM-DSB-SC)
A modulating signal s(t) [with Fourier transform S( f ) ] is applied
to a double-sideband suppressed-carrier (DSB-SC) modulator
operating at a carrier frequency of

1
Tutorial 2
Deterministic Signal Analysis
Principles of Communications
2
Problem 1 (Fourier Spectrum)
Derive the Fourier spectrum of the following signals:
Acos(2 f t) t / 2
0
1) Truncated sinusoidal signal: s(t) =
0
elsewhere
where f0 is an integer mu

1
Tutorial 3
Amplitude Modulation (AM)
Principles of Communications
2
Problem 1 (AM-DSB-SC)
A modulating signal s(t) [with Fourier transform S( f ) ] is applied
to a double-sideband suppressed-carrier (DSB-SC) modulator
operating at a carrier frequency of

1
Tutorial 2
Deterministic Signal Analysis
Principles of Communications
2
Problem 1 (Fourier Spectrum)
Derive the Fourier spectrum of the following signals:
A cos 2 f 0t t / 2
1) Truncated sinusoidal signal: s(t ) =
0
elsewhere
where f0 is an integer mu

Solutions to EE3008 Tutorial 1 Problems
Problem 1: Using the time scaling property, we have
s(t) S(f ).
Then, using the time shift property, we have
s[(t 1)] ej2f S(f )
and
s[(t + 1)] ej2f S(f ).
Therefore, using the linearity property, we obtain
s(1 t) +

EE3008 Principles of Communications
Tutorial 1
Problem 1: Given that s(t) has the Fourier transform S(f ), express the Fourier transform
of the signal x(t) = s(1 t) + s(1 t) in terms of S(f ).
Problem 2: Compute the Fourier transform of each of the follow

1
Lecture 8. Digital Communications
Part III. Digital Demodulation
Binary Detection
M-ary Detection
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 8
2
Digital Communications
Analog Signal
Bit sequence
t
Source
SOURCE
00

Solutions to EE3008 Quiz 3 Problems
Problem 1:
(a) Since X(t) is a white process, the power spectrum of X(t) is given by
GX (f ) =
N0
.
2
The transfer function of the LTI system is obtained as
1
, |f |
2
H(f ) =
0, otherwise.
Since X(t) is a WSS process

Solutions to EE3008 Quiz 2 Problems
Problem 1:
(a) The carrier frequency is fc = 107 Hz.
(b) By definition, the instantaneous phase of this FM signal is
7
(t) = 2 10 t + 50
Z t
sinc( )d .
Therefore, the instantaneous frequency is
f (t) =
1 d(t)
= 107 + 50

Name: _
Student ID: _
Signature: _
CITY UNIVERSITY OF HONG KONG
Semester B 2014/2015
EE3008: Principles of Communications
Quiz 2
1.
2.
3.
4.
Time allowed: One hour
Total number of problems: 3
Total marks available: 35
This paper may not be retained by can

Solutions to EE3008 Quiz 1 Problems
Problem 1:
(a) H(f ) = 1.
(b) Given the Fourier transform pair
(
s(t) =
A, |t| /2
S(f ) = A sinc(f )
0, otherwise
and using the duality property, we have
(
s(t) = A sinc(t ) S(f ) =
A, |f | /2
0, otherwise.
Then, letti

Name: _
Student ID: _
Signature: _
CITY UNIVERSITY OF HONG KONG
Semester B 2014/2015
EE3008: Principles of Communications
Quiz 1
1.
2.
3.
4.
Time allowed: One hour
Total number of problems: 3
Total marks available: 30
This paper may not be retained by can

1
Variance of Sampled AWGN
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 8
2
Consider that AWGN n(t) passes through a filter h(t) and is
sampled at t0. Suppose that the two-sided power spectral density
of n(t) is N0/2 an

1
Derivation of Power Spectrums of Digital
Baseband & Bandpass Modulated Signals
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 7
2
1. Power Spectrum of Digital Baseband
Modulated Signal
For a digital baseband modulated s

1
Lecture 5. Random Signal Analysis
Random Variables and Random Processes
Signal Transmission through a Linear System
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 5
2
Discrete Random Variables
A discrete random varia

1
Lecture 2. Deterministic Signal
Analysis
Fourier Transform
Energy Spectrum, Power Spectrum and Signal Bandwidth
Signal Transmission through a Linear System
Lin Dai (City University of Hong Kong)
EE3008 Principles of Communications
Lecture 2
2
Signals

1
Lecture 3 - Analog Communications
Part I: Amplitude Modulation (AM)
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 3
2
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 3
3
Radio broadcast

1
Lecture 4. Analog Communications
Part II. Frequency Modulation (FM)
Angle Modulation (FM and PM)
Spectral Characteristics of FM signals
FM Modulator and Demodulator
Department of Electronic Engineering
EE3008 Principles of Communications
Lecture 4
2

1
Tutorial 9
Principles of Communications
2
Problem 1 (Matched Filter)
Consider the transmitted signal:
s (t) = 1, if b = 1
1
1
s(t) =
s2 (t) = 0, if b1 = 0
0 t
1) Draw the impulse response of the corresponding matched
filter.
2) Draw the output of t

1
Tutorial 8
Principles of Communications
2
Problem 1 (Bandpass Modulation)
Digital data is to be transmitted over a bandpass channel with
bandwidth 1MHz. Determine the maximum bit rate that can be
supported by the channel with 90% in-band power in each o

1
Tutorial 7
Principles of Communications
2
Problem 1 (Gray Code)
A signal with dynamic range (-8V, 8V) is applied to a 3-bit
midriser. Assume the samples have the following amplitudes:
4.6V, 0.8V, -0.2V, 1.6V, 3.4V, -6.4V
Sketch the resulting sequence of

1
Tutorial 8
Principles of Communications
2
Problem 1 (Bandpass Modulation)
Digital data is to be transmitted over a bandpass channel with
bandwidth 1MHz. Determine the maximum bit rate that can be
supported by the channel with 90% in-band power in each o

1
Tutorial 6
Sampling and Quantization
Principles of Communications
2
Problem 1
A baseband signal x(t) is sampled with a rectangular pulse train p(t),
producing an output xs(t), as shown in Fig. 1(a). The sampling process
here is termed natural sampling.

1
Tutorial 9
Principles of Communications
2
Problem 1 (Matched Filter)
Consider the transmitted signal:
s (t) = 1, if b = 1
1
1
s(t) =
s2 (t) = 0, if b1 = 0
0 t
1) Draw the impulse response of the corresponding matched
filter.
2) Draw the output of t