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

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) +

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

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 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 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

EE 3008. Receiver Design Tutorial Questions
Q1) Suppose we are transmitting a variable v, which can be either 1 or 0. Suppose during the
transmission v is distorted by a Gaussian random variable n with zero mean and variance 2,
so the receiver actually re

EE 3008 Chapter 5 Tutorial Questions
Q1) Consider data rate 10 kbps and carrier frequency 1MHz. Roughly sketch the amplitude
spectrum for (a) BPSK modulation; and (b) On-off ASK modulation.
Q2)
A BPSK has carrier signal Abcos(2109t)V where b=+1 and -1. Le

Q1)
EE 3008. Random Process Tutorial Questions
A coin is tossed three times. What is the probability of two heads and one tail?
Given that the random variable X has density function
0 < x <1
2x
f ( x)
otherwise
0
Find Pr(0.5<x<3/4) and Pr(-0.5<x<0.5).
Q2

EE 3008. AD-DA Conversion Tutorial Questions
Q1) Consider a multi-user PCM system. For circuit speed limitation, a pulse requires a minimum
duration of 1s. If the input bandwidth of each user (before sampling) is 3kHz and the
quantization level is 16, cal

1
px ( x)
2 2
EE 3008. Receiver Design Tutorial Solutions
Q1)
Prcfw_x>1.5
Prcfw_x<0.5
0
1/2
Prcfw_1 0
2
2
e
2
2
correct region for v=1
y
( x1)2
1
dx
x
1.5
1
error region for v=1
0.5
e
( x 1)2
2 2
x1
0.5/
1 2y
1 2y
e dy
e dy Q(0.5/ )
2
2
0.5/
2
2
Thi

EE 3008. Baseband Modulation Tutorial Questions
Q1) A sequence 01 is represented by the following signal. Find the
energy spectrum of this signal.
s01(t)
A
-A
2
t
Q2) A sequence 11 is represented by the following signal. Find the
energy spectrum of this s

Q1)
Q2)
EE 3008. Random Process Tutorial Solutions
All possible outcomes are listed below,
HHH HHT HTH HTT THH THT TTH TTT
There three events with two heads and one tail, i.e.,
HHT HTH THH
Therefore the probability is 3/8.
Prcfw_0.5 x 3 / 4
Prcfw_0.5 x 0

EE 3008. Baseband DM Tutorial Solutions
Q1) When the circuit speed is considered, 1s is required for one bit. Since the input bandwidth
is 3kHz, the Nyquist sampling rate = 23k = 6kHz. The sampling interval = 1/6k = 167s. For
each sample, 16 quantization

EE 3008 Chapter 6 Tutorial Solutions
AM Solutions
Q1) (i) Now fc = 200 Hz. The modulated signal is given by
g(t) = f(t)cos(2fct)=cos(100t)cos(400t)=0.5cos(300t)+0.5cos(500t)
G(f)=(1/4)[(f-150)+ (f+150)+ (f-250)+ (f+250)]
1/2 G(f)
-50
50
-250
f
G(f)
-150
1

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

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 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 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
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
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 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 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
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
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