This document provides an overview of RF transceiver systems and related concepts. It begins with definitions of dB, phasors, and modulation techniques. It then discusses transmitter and receiver architectures, moving from basics to more advanced concepts. Key topics covered include I/Q modulation, linear modulation, transmitter architectures using either I/Q or polar modulation, and the use of phasors in various applications from circuit analysis to communications systems.
In telecommunications and signal processing, frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. This contrasts with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency remains constant.
In analog frequency modulation, such as FM radio broadcasting of an audio signal representing voice or music, the instantaneous frequency deviation, the difference between the frequency of the carrier and its center frequency, is proportional to the modulating signal.
In this presentation we discuss about a particular type of analog communication waves that is wideband frequency modulation. In this slide, its expression is discussed along with graphical visuals. Not forgetting its power and bandwidth as well. We also see the use of bessel function and the block diagrams that help to form this type of waves.
We have implemented a multiple precision ODE solver based on high-order fully implicit Runge-Kutta(IRK) methods. This ODE solver uses any order Gauss type formulas, and can be accelerated by using (1) MPFR as multiple precision floating-point arithmetic library, (2) real tridiagonalization supported in SPARK3, of linear equations to be solved in simplified Newton method as inner iteration, (3) mixed precision iterative refinement method\cite{mixed_prec_iterative_ref}, (4) parallelization with OpenMP, and (5) embedded formulas for IRK methods. In this talk, we describe the reason why we adopt such accelerations, and show the efficiency of the ODE solver through numerical experiments such as Kuramoto-Sivashinsky equation.
This presentation covers noise performance of Continuous wave modulation systems; It explains modelling of white noise , noise figure of DSB-SC, SSB, AM, FM system
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
1. Multiband RF Transceiver System
Chapter 1
From Basics to RF Transceivers
李健榮 助理教授
Department of Electronic Engineering
National Taipei University of Technology
2. Outline
• Definition of dB
• Phasor
• Modulation
• Transmitter Architecture
• Demodulation
• Receiver Architecture
• From Fourier Transform to Modulation Spectrum
Department of Electronic Engineering, NTUT2/44
3. Definition of dB
• , where
• Power gain
• Voltage gain
• Power (dBW)
• Power (dBm)
• Voltage (dBV)
• Voltage (dBuV)
( )dB 10 log G= ⋅ ( )aG
b
=
2
1
10 log
P
P
= ⋅
2
1
20 log
V
V
= ⋅
( )10 log
1-W
P= ⋅
( )10 log
1-mW
P= ⋅
( )20 log
1-Volt
V= ⋅
( )20 log
1- V
V
µ= ⋅
Relative
(Ratio, unitless, dB)
Absolute
(Have unit, dBW, dBm, dBV…)
Department of Electronic Engineering, NTUT3/44
4. In some textbooks, phasor may be
represented as
Euler’s Formula
• Euler’s Formula states that: cos sinjx
e x j x= +
( ) ( ) ( )
{ } { }cos Re Rej t j j t
p p pv t V t V e V e eω φ φ ω
ω φ +
= ⋅ + = ⋅ = ⋅
( )cos sin
def
j
p p pV V e V V jφ
φ φ φ= ⋅ = ∠ = +• Phasor :
Don’t be confused with Vector which is commonly denoted as .A
phasor
A real signal can be represented as:
V
V
( ) ( )cospv t V tω φ= ⋅ +
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5. Euler’s Trick on the Definition of e
2 3
lim 1 1
1! 2! 3!
n
x
n
x x x x
e
n→∞
= + = + + + +
…
x jx=
( ) ( )
2 3 2 4 3 5
1 1
1! 2! 3! 2! 4! 3! 5!
jx jx jxjx x x x x
e j x
= + + + + = − + − + + − + − +
… … …
• Euler played a trick : Let , where 1j = −
1
lim 1
n
n
e
n→∞
= +
6/33
2 4
cos 1
2! 4!
x x
x = − + − +…
3 5
sin
3! 5!
x x
x x= − + − +…
cos sinjx
e x j x= +
cos sinjx
e x j x−
= −
cos
2
jx jx
e e
x
−
+
=
sin
2
jx jx
e e
x
j
−
−
=
• Use and
we have
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6. Coordinate Systems
x-axis
y-axis
x-axis
y-axis
P(r,θ)
θ
r
P(x,y)
2 2
r x y= +
1
tan
y
x
θ −
=
cosx r θ=
siny r θ=
Cartesian Coordinate System Polar Coordinate System
(x,0)
(0,y)
( )cos ,0r θ
( )0, sinr θ
Projection
on x-axis
Projection
on y-axis
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8. x
θ
0
π/2
π
3π/2
Cosine Waveform
x-axis
y-axis
θ
Go along the circle, the projection
on x-axis results in a cosine wave.
Sinusoidal waves relate to a Circle
very closely.
Complete going along the circle to
finish a cycle, and the angle θ
rotates with 2π rads and you are
back to the original starting-point
and. Complete another cycle again,
sinusoidal waveform in one period
repeats again. Keep going along the
circle, the waveform will
periodically appear.
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9. Complex Plan (I)
It seems to be the same thing with x-y plan, right?
• Carl Friedrich Gauss (1777-1855) defined the complex plan.
He defined the unit length on Im-axis is equal to “j”.
A complex Z = x + jy can be denoted as (x, yj) on the complex plan.
(sometimes, ‘j’may be written as ‘i’which represent imaginary)
Re-axis
Im-axis
Re-axis
Im-axis
P(r,θ)
θ
r
P(x,yj)
2 2
r x y= +
1
tan
y
x
θ −
=
cosx r θ=
siny r θ=
(x,0j)
(0,yj)
( )cos ,0r θ
( )0, sinr θ
( )1j = −
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10. Complex Plan (II)
Re-axis
Im-axis
1
Every time you multiply something by j, that thing will rotate 90 degrees.
1j = − 2
1j = − 3
1j = − − 4
1j =
1*j=j
j
j*j=-1
-1
-j
-1*j=-j -j*j=1
(0.5,0.2j)
(-0.2, 0.5j)
(-0.5, -0.2j)
(0.2, -0.5j)
• Multiplying j by j and so on:
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11. Sine Waveform
Re-axis
Im-axis
P(x,y)
x
y
r
θ θθ
y = rsinθ
θ
0 π/2 π 3π/2 2π
To see the cosine waveform, the same operation can be applied to trace out
the projection on Re-axis.
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12. Phasor Representation (I) – Sine Basis
( ) ( ) { } { }sin Im Imj j t j j
sv t A t Ae e Ae eφ ω φ θ
ω φ= + = =
Re-axis
Im-axis
P(A,ϕ)
y = Asinϕ
θ
0 π/2 π 3π/2 2π
ϕ
tθ ω=
Given the phasor denoted as a point on the complex-plan, you should know it
represents a sinusoidal signal. Keep this in mind, it is very important!
time-domain waveform
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13. Phasor Representation (II) – Cosine Basis
( ) ( ) { } { }cos Re Rej j t j j
sv t A t Ae e Ae eφ ω φ θ
ω φ= + = =
Re-axis
Im-axis
P(A, ϕ)
y = Acos ϕ
θ
0 π/2 π 3π/2 2π
ϕ
tθ ω=
time-domain waveform
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14. Phasor Representation (III)
( ) ( ) { }1
1 1 1 1sin Im j j t
v t A t Ae eφ ω
ω φ= + =
Re-axis
Im-axis
P(A1, ϕ1)
ϕ1
P(A2, ϕ2)
P(A3, ϕ3)
θ
0 π/2 π 3π/2 2π
tθ ω=
A1sin ϕ1
( ) ( ) { }2
2 2 2 2sin Im j j t
v t A t A e eφ ω
ω φ= + =
( ) ( ) { }3
3 3 3 3sin Im j j t
v t A t A e eφ ω
ω φ= + =
A2sin ϕ2
A3sin ϕ3
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15. Phasor Everywhere
• Circuit Analysis, Microelectronics:
Phasor is often constant.
• Field and Wave Electromagnetics, Microwave Engineering:
Phasor varies with the propagation distance.
• Communication System:
Phasor varies with time (complex envelope, envelope, or
equivalent lowpass signal of the bandpass signal).
( ) ( )5cos 1000 30sv t t= + 5 30sV = ∠
( ) ( ) ( ) ( ) ( )
{ }, cos cos Re j x t j x t
v x t A x t B x t Ae Beβ ω β ω
β ω β ω − − +
= − + + = +
( ) j x j x
V x Ae Beβ β−
= +
( ){ }Re j t
V x e ω
=
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16. Modulation
• Why modulation?
Communication
Bandwidth
Antenna Size
Security, avoid Interferes, etc.
Voice
Electric signal
Audio
Equipment
Audio
Equipment
Modulator Demodulator
Electric signal
Voice
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17. Amplitude Modulation
( ) ( ) cos2m BB cs t s t A f tπ= ⋅
Baseband real signal
Voice
Electric signal
Audio
Equipment
Audio
Equipment
Modulator Demodulator
Electric signal
Voice
( )BBs t
cos2 cA f tπ
Carrier (or local)
High-frequency sinusoid
Amplitude-modulated signal
(AM signal)
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18. Frequency Modulation
( ) ( ){ }cos 2m c f BBs t A f K s t tπ = + ⋅
Voice
Electric signal
Audio
Equipment
Audio
Equipment
Modulator Demodulator
Electric signal
Voice
Baseband real signal
( )BBs t
cos2 cA f tπ
Carrier (or local)
High-frequency sinusoid
Frequency-modulated signal
(FM signal)
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19. Phase Modulation
Voice
Electric signal
Audio
Equipment
Audio
Equipment
Modulator Demodulator
Electric signal
Voice
( ) ( )cos 2m c p BBs t A f t K s tπ = +
( )cos 2 c BBA f t tπ φ= +
Baseband real signal
( )BBs t
cos2 cA f tπ
Carrier (or local)
High-frequency sinusoid
Phase-modulated signal
(PM signal)
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20. Linear Modulation
( ) ( ) ( )cos 2m BB c BBs t A t f t tπ φ= ⋅ +
Voice
Electric signal
Audio
Equipment
Audio
Equipment
Modulator Demodulator
Electric signal
Voice
Baseband real signal
( )BBs t
cos2 cA f tπ
Carrier (or local)
High-frequency sinusoid
Linear-modulated signal
( )BBs t ( ) ( ), ?BB BBA t tφ
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21. Linear Modulation
• Consider a modulated signal
( ) ( ) ( ) ( ) ( )
{ }2
cos 2 Re c BBj f t t
m BB c BB BBs t A t f t t A t e
π φ
π φ
+
= ⋅ + = ⋅
( ) ( )
( ) ( ) ( ){ }2 2
Re Re cos sinBB c cj t j f t j f t
BB BB BB BBA t e e A t t j t e
φ π π
φ φ = ⋅ = ⋅ +
( ) ( ) ( )
( ) ( ) ( )cos sinBBj t
l BB BB BB BBs t A t e A t t j tφ
φ φ= ⋅ = ⋅ +
( ) ( ) ( ) ( ) ( ) ( )cos sinBB BB BB BBA t t jA t t I t jQ tφ φ= ⋅ + ⋅ = +
( ) ( ) ( ) ( ){ }Re cos2 sin2m c cs t I t jQ t f t j f tπ π= + ⋅ +
( ) ( )cos2 sin 2c cI t f t Q t f tπ π= −
Time-varying phasor (information in both amplitude and phase)
( )BBs t : real
( )ls t : complex
Modulated signal is the linear combination of I(t), Q(t), and the carrier. Thus the linear modulator
is also called “I/Q Modulator,” and it is an universal modulator.
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22. Linear Modulator
• The modulator accomplishes the mathematical operation.
( ) ( ) ( ) ( ) ( ){ }Re cos sin cos2 sin 2m BB BB BB c cs t A t t j t f t j f tφ φ π π= ⋅ + +
( ) ( ) ( ) ( )cos cos2 sin sin 2BB BB c BB BB cA t t f t A t t f tφ π φ π= −
( ) ( )cos2 sin 2c cI t f t Q t f tπ π= −
( )I t
cos ctω
sin ctω−
( )Q t
( )ms t
( )I t
cos ctω
sin ctω
( )Q t
( )ms t
+
− 90
( )I t
cos ctω
( )Q t
( )ms t
Department of Electronic Engineering, NTUT
I component Q component
I channel Q channel
22/44
23. Transmitter Architecture (I)
• Linear Transmitter
90
( )I t
cos ctω
( )Q t
( )ms t
Power Amplifier
(PA)
Antenna
Baseband
Processor
90
cos ctω
( )ms t
Power Amplifier
(PA)
Antenna
Matching /
BPF
Matching
( )I t
( )Q t
Baseband
Processor
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24. Transmitter Architecture (II)
• Polar Transmitter
( ) ( ) ( ) ( ){ } ( ) ( )
{ }22
cos 2 Re Re c BBc
j f t tj f t
m BB c BB l BBs t A t f t t s t e A t e
π φπ
π φ
+
= ⋅ + = ⋅ = ⋅
( )BBA t
cos ctω
( )ms t
Switching-mode
PA
Antenna
Phase
Modulator
Matching
( )BBA t
( )BB tφ
Baseband
Processor
Amplitude
Modulator
• Linear regulator
• PWM modulator
• Class-S modulator
• Linear modulator to generate PM signal
• Frequency synthesizer or PLL-based PM modulator
• Analog scheme: EER
( )
{ }2
Re c BBj f t t
e
π φ+
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25. Linear Demodulation
( ) ( ) ( ) ( ) ( )cos 2 cos2 sin2m BB c BB c cs t A t f t t I t f t Q t f tπ φ π π= ⋅ + = −
( ) ( ) ( ) ( ) ( ) ( ) ( )2 1 1
cos2 cos 2 sin2 cos2 cos4 1 sin4 sin0
2 2
m c c c c c cs t f t I t f t Q t f t f t I t f t Q t f tπ π π π π π= − ⋅ = ⋅ + − ⋅ +
( ) ( ) ( ) ( ) ( ) ( ) ( )2 1 1
sin2 cos2 sin2 sin 2 sin4 sin0 1 cos4
2 2
m c c c c c cs t f t I t f t f t Q t f t I t f t Q t f tπ π π π π π− = − + = − ⋅ + + ⋅ −
( ) ( ) ( )cos4 sin 4
2 2 2
c c
I t I t Q t
f t f tπ π
= + −
( ) ( ) ( )sin4 cos4
2 2 2
c c
Q t I t Q t
f t f tπ π
= − +
?
Receiver
( )ms t ( )BBs t
Received modulated signal:
Multiplied by “cosine”:
Multiplied by “−−−− sine”:
High-frequency components
(should be filtered out)
High-frequency components
(should be filtered out)
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26. Linear Demodulator
( )I t
cos ctω
sin ctω−
( )Q t
( )ms t
LPF
LPF
( )I t
( )Q t
( )ms t
LPF
LPF
90
cos ctω
( ) ( ) ( )
( ) ( )BBj t
l BBs t A t e I t jQ t
φ
= ⋅ = +
( ) ( ) ( )2 2
BBA t I t Q t= +
( )
( )
( )
1
tanBB
Q t
t
I t
φ −
=
Baseband
Processing
Original Information (or data)
( )I t
( )Q t
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27. Receiver Architecture
• Linear Receiver (direct conversion)
90
( )I t
cos ctω
( )Q t
( )ms t
Low Noise Amplifier
(LNA)
Baseband
Processor
LPF
LPF
Matching /
BPF
90
( )I t
cos ctω
( )Q t
( )ms t
Low Noise Amplifier
(LNA)
Baseband
Processor
LPF
LPF
Matching
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28. Digital Modulation
• I(t) and Q(t) for digital transmission?
• Assume that I(t) and Q(t) are pulses at TX, I(t) and Q(t)
waveforms will be recovered ideally after the demodulation
process, of course, pulses.
Department of Electronic Engineering, NTUT
( ) ( ) ( )cos2 sin 2m c cs t I t f t Q t f tπ π= −
( )I t
cos ctω
sin ctω−
( )Q t
( )ms t
LPF
LPF
( )I t
cos ctω
sin ctω−
( )Q t
TX RX
Assume the LPF has a
sufficiently wide bandwidth to
recover the pulse waveform.
28/44
29. • A Quadrature Phase Shift Keying (QPSK) signal is a good
example.
Quadrature Phase Shift Keying
( )I t
( )Q t
( )1,1
( )1, 1−( )1, 1− −
( )1,1−
cA+
cA+cA−
cA−
Constellation
( )I t
cos ctω
sin ctω−
( )Q t
S/P
Converter
Binary
Baseband
Data( )I t
( )Q t
Binary
Baseband
Data
bT
2 bT
t
S/P Converter
The linear combination shows that the QPSK signal
has 4 different phase states (1 symbol = 2 bits = 4
states).
Department of Electronic Engineering, NTUT
Symbol
29/44
30. • Phase transition in QPSK signal due to simultaneous transition
of I(t) and Q(t).
Phase Transition
( )I t
( )Q t
S/P
Converter
Binary
Baseband
Data
( )I t
( )Q t
t
( )I t
( )Q t
( )1,1
( )1, 1−( )1, 1− −
( )1,1−
cA+
cA+cA−
cA−
Constellation
Constant
envelope
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31. Bandwidth Consideration (I)
• A rectangular waveform has many frequency components
covering within a wide bandwidth. For many reasons, the
modulation spectrum occupying such a wide bandwidth is not
preferable.
( ) ( ) ( )cos2 sin 2m c cs t I t f t Q t f tπ π= −
( )I t
cos ctω
sin ctω−
( )Q t
TX
f
f
f
( )mS f
How to limit the
bandwidth?
cf
cf
f
0
0
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32. Bandwidth Consideration (II)
• Is that good to limit the bandwidth at passband?
( )I t
cos ctω
sin ctω−
( )Q t
TX
BPF
cf
f
channel
f
( )I t
cos ctω
sin ctω−
( )Q t
BPF2
BPF1
BPFn
channel
f
channelchannel
Requiring many BPFs for each channel is impractical
selector
cf
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33. Bandwidth Consideration (III)
• Limit the bandwidth at baseband – Pulse Shaping
( )I t
cos ctω
sin ctω−
( )Q t
LPF
LPF
f
t
0
f
t
0
f0
f0
cf
f
The low-pass filter is use to shape the
waveform, thus called “pulse shaping
filter,” or “shaping filter.”
Constant envelope
(before shaping)
180 18090
Time-varying envelope
(after shaping)
Smooth the sharp transition
( )1,1
( )1,1−
( )Q t
( )I t
( )1, 1−( )1, 1− −
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34. Band-limiting and Inter Symbol Interference (I)
• Nyquist Filter :
Produce pulse shapes with no ISI at each sampling instant
Brick-wall LPF
IFT
Sinc shape
Raised Cosine Filter
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35. Band-limiting and Inter Symbol Interference (II)
• Gaussian Filter :
Time domain response is Gaussian as well, it exhibits no overshot or ringing in the
time domain. This smooth well-behaved impulse response results in very little ISI
Reduce bandwidth : Smaller BT causes even faster spectral roll-off , but this has a
price, smaller BT cause more ISI.
Relative bandwidth BT = (filter BW) / (Bite rate)
Power spectra of MSK and GMSK Signals for varying BT
BT=0.2
BT=0.25
BT=0.3
Impulse response
MSK : BT is infinite
(no filter)
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36. Optimum Receiver
( )I t
cos ctω
sin ctω−
( )Q t
( )ms t
LPF
LPF
( )I t
cos ctω
sin ctω−
( )Q t
LPF
LPF
TX RX
Matched Filter
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37. Picture of a Practical Transceiver
( )I t
cos ctω
sin ctω−
( )Q t
LPFFilter
Filter
DAC
DAC LPF
Digital Processor
Digital pulse shaping filter
Waveform recovery filter
for DAC
Data (bits)
Waveform
(digital, M-bits)
Quantized Waveform (analog) Recovered Waveform (analog)
( )I t
cos ctω
sin ctω−
( )Q t
( )ms t
LPF
LPF
Filter
Filter
Digital Processor
Matched filter or
correlator
ADC
ADC
Demodulated Waveform (analog)
Sampled Waveform
(digital)
Decision
Decision
Data (bits)
Mixing spurs remover
Encoder and decoder are not
included here for simple.
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38. Modulation in Frequency Domain
• Spectrum of a Real Signal
• AM, PM, and Linear Modulated Signal
• Concept of Complex Envelope
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39. Modulation Spectrum (I)
• From Euler’s Formula :
• AM signal (DSB-SC)
cos
2
jx jx
e e
x
−
+
=
A “real signal” is composed of positive and negative frequency components.
( ) ( )cos2m cs t A t f tπ=
Two-sided amplitude frequency spectrum
( ) ( )2 1000 2 10001
50cos 2 1000
2
j t j t
t e eπ π
π × − ×
× = +
2525
0 Hz 1 kHz1 kHz−
f
One-sided amplitude frequency spectrum
50
0 Hz 1 kHz
( )50cos 2 1000tπ ×
f
t( ) ( )BBs t A t=
f
f
cf0 Hzcf−
0 Hz
USBLSB
USBLSBLSBUSB
cos2 cf tπ
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“real signal”
39/44
40. Phase
Modulator
Modulation Spectrum (II)
t( )BBs t
f
0 Hz
USBLSB
cos2 cf tπ
( ) ( )2 2
2 2
c cj t j tj f t j f tA A
e e e e
φ φπ π− −
= +
( ) ( )( )cos 2m cs t A f t tπ φ= +
( )
{ } ( )
{ }2 2
Re Rec c
j f t t j t j f t
A e A e e
π φ φ π+
= ⋅ = ⋅
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“real signal”
f
cf0 Hzcf−
USBLSBLSBUSB
“complex”“complex” “real”
• PM signal
Complex conjugate
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41. Modulation Spectrum (III)
I/Q
Modulator
t( )BBs t
f
0 Hz
USBLSB
cos2 cf tπ
( ) ( ) ( ) ( )2 2
2 2
c cj t j tj f t j f tA t A t
e e e eφ φπ π− −
= +
( ) ( ) ( )( )cos 2m cs t A t f t tπ φ= +
( ) ( )
{ }2
Re cj t j f t
A t e e
φ π
= ⋅
“real signal”
• I/Q modulated signal
( )I t
( )Q t
f
cf0 Hzcf−
USBLSBLSBUSB
“complex”“complex” “real”
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Complex conjugate
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42. Concept of the Complex Envelope (I)
• Bandpass real signal :
( ) ( ) ( )( )
( ) ( ) ( ) ( )2 2
cos 2
2 2
c cj t j tj f t j f t
m c
A t A t
s t A t f t t e e e e
φ φπ π
π φ − −
= + = +
( ) ( )
( ) ( )2 21 1
2 2
c cj t j tj f t j f t
A t e e A t e eφ φπ π− −
= +
( )ls t ( )ls t∗
( )lS f∗
( )lS f
Complex timed value
Spectrum
( ) ( )
( ) ( )2 21 1
2 2
c cj t j tj f t j f t
A t e e A t e eφ φπ π− −
= +
( ) 2 cj f t
ls t e π
⋅ ( ) 2 cj f t
ls t e π−∗
⋅
( )l cS f f−
Complex timed value
Spectrum
( ) ( ) ( )
1
2
m l c l cS f S f f S f f∗
= − + − −
f
cf0 Hzcf−
USBLSBLSBUSB
( )
1
2
l cS f f−( )
1
2
l cS f f∗
− −
Spectrum of the bandpass signal
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( )l cS f f∗
− −
43. Concept of the Complex Envelope (II)
• Equivalent low-pass signal (complex envelope):
f
0 Hz
( )lS f
cfcf−
( ) 21
2
cj f t
ls t e π
⋅( ) 21
2
cj f t
ls t e π−∗
⋅
( ) ( ) ( )
( ) ( )j t
ls t A t e I t jQ t
φ
= = +
( ) ( ) ( )
1
2
m l c l cS f S f f S f f∗
= − + − −
f
cf0 Hzcf−
USBLSBLSBUSB
( ) ( )
1
2
I t jQ t+
Spectrum of the bandpass signal
( ) ( )
1
2
I t jQ t−
( )ms t
( ) ( ) ( )
( ) ( )BBj t
ls t A t e I t jQ t
φ
= = +
complex envelope
( ) ( ) ( ) ( ) ( ) 2
cos 2 Re cj t j f t
m cs t A t f t t A t e e
φ π
π φ = ⋅ + = ⋅
( ) ( ){ }2
Re cj f t
I t jQ t e π
= +
complex envelope
carriercarrier2 cj f t
e π
carrier
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44. Summary
• In this chapter, the phasor was introduced to manifest itself in
the mathematical operation for communication engineering.
• A modulated signal is a linear combination of I(t), Q(t), and
the carrier. This mathematical combination can be realized
with a practical circuitry, say, “modulator.”
• The demodulation is the decomposition of the modulated
signal, which is the reverse process to recover the baseband
signal I(t) and Q(t).
• The modulated signal can be viewed as a complex envelope
carried by a sinusoidal carrier. With this equivalent lowpass
form to represent a bandpass system, the mathematical
analysis can be easily simplified.
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