Lec. 1: Intro.
EECE233: Signals and Systems
Lecture 1:
Introduction
Prof. Kyung-Tae Kim
Department of Electrical Engineering
POSTECH
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Lec. 1: Intro.
EECE233: Signals and Systems
Course Introduction
• Class: Mon./Wed. 11:00-12:15
• Email: kkt@postech.ac.kr
• TA:
▪ Sangbeom Ha (sangbeomha@postech.ac.kr)
▪ Jeongmin Ryu (yujm1217@postech.ac.kr)
▪ Bonyoung Koo (kooby@postech.ac.kr)
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Lec. 1: Intro.
EECE233: Signals and Systems
Course Introduction
• Evaluation:
▪ Homework: 20%
▪ Midterm exam: 40%
▪ Final exam: 40%
• Lecture slides will be uploaded on PLMS
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Lec. 1: Intro.
EECE233: Signals and Systems
Course Introduction
• Reference materials:
▪ Some selected chapters of these books will be covered
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Lec. 1: Intro.
EECE233: Signals and Systems
Course Outline
• Basics of Signals
• Basics of Systems
• Linear Time-Invariant (LTI) Systems
• Fourier Transform & Fourier Series
• Properties of Fourier Transform & Fourier Series
• Applications of Fourier Transform & Fourier Series
• The Laplace Transform
• The 𝑧-Transform
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Lec. 1: Intro.
EECE233: Signals and Systems
Contents
• Introduction to Signals and Systems
• Classification of Signals
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Lec. 1: Intro.
EECE233: Signals and Systems
What is a Signal ?
• Signal
▪ A function of one or more variables that conveys information
on the nature of a physical phenomena
• Examples
▪ Speech signal, visual (image) signal
▪ Heartbeat of a patient, weather forecast
▪ Daily fluctuations in the prices of stocks and commodities
▪ Electromagnetic waves
• One-dimensional (1-D) signals
▪ Speech signals
• Multi-dimensional signals
▪ Image
speech
image
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EECE233: Signals and Systems
What is a System?
• System
▪ An entity that manipulates one or more signals to accomplish
a function, thereby yielding new signals
• Example
▪ Automatic speaker recognition systems
▪ Communication systems
▪ Control systems
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Lec. 1: Intro.
EECE233: Signals and Systems
Communication Systems
• Elements of a communication system
▪ Transmitter: Convert the message signal produced by a
source of information into a form suitable for transmission
over the channel
▪ Channel: Optical fiber, coaxial cable, satellite channel, mobile
radio channel
▪ Receiver: Reconstruct a recognizable form of the original
message signal and deliver it to its destination
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Lec. 1: Intro.
EECE233: Signals and Systems
Communication Systems
• Modulation
▪ Process of converting the message signal into a form that is
compatible with the transmission characteristics of the
channel
• Digital communication systems
▪ Sampling: Convert the message signal into a sequence of
numbers, with each number representing the amplitude of
the message signal at a particular instant of time
→ Discrete-time signals
▪ Quantization: Represent each number produced by the
sampler to the nearest level selected from a finite number of
discrete amplitude levels
→ Digital signals
▪ Coding: Represent each quantized sample by a code word
made up of a finite number of symbols
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Lec. 1: Intro.
EECE233: Signals and Systems
Discrete-Time Signals vs. Digital Signals
Discrete-time signals
Quantization
Digital signals
3-bit quantization error
8-bit quantization error
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Lec. 1: Intro.
EECE233: Signals and Systems
Communication Systems
• Digital communication systems
▪ Data compression: Remove redundant information from the
message signal, providing efficient utilization of the channel
▪ Example: Joint Photographic Experts Group (JPEG)
1001101010
1011101010
1010101011
010111001⋯
DCT
Quantizer
Encoder
[Image source] B. J. Erickson, “Irreversible Compression of Medical Images,” J. Digital Imaging
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Lec. 1: Intro.
EECE233: Signals and Systems
Communication Systems
• Digital communication systems
▪ Channel encoding: Insert redundant elements into the code
word in a controlled manner in order to protect against noise
and interfering signals in the channel
▪ Example: Repetition code with rate 1/3
010
010
No
Channel
Coding
Channel
Coding
(3 Repetition)
010
Communication
with bit errors
2-bit error
001
2-bit error
000111000 Communication 000101001
with bit errors
No
Channel
Decoding
001
Channel
Decoding
010
(3 Repetition)
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Lec. 1: Intro.
EECE233: Signals and Systems
Control Systems
• Examples
▪ Aircraft autopilots, autonomous vehicles, automobile engines,
machine tools, nuclear reactors, and robots
• Two important factors
▪ Response: A plant is said to produce a satisfactory response if
its output follows or specified reference input
▪ Robustness: Robust if it regulates its objects well, despite the
presence of external disturbances
• Feedback control system (Closed loop control system)
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Lec. 1: Intro.
EECE233: Signals and Systems
Remote Sensing
• Remote sensing
▪ Process of acquiring information about an object of interest
without being in physical contact with it
• Types of signals
▪ Electromagnetic waves, acoustic waves, magnetic waves,
infrared waves, etc.
• Types of sensors
▪ Radar sensors: Surface physical properties (e.g., roughness,
moisture, and dielectric constant)
▪ Infrared sensors: Thermal properties of an object
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Lec. 1: Intro.
EECE233: Signals and Systems
Radar sensing
• SAR imaging
E/O
SAR image
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Lec. 1: Intro.
EECE233: Signals and Systems
Biomedical Signal Processing
• Biomedical Signals
▪ Electrocardiogram (ECG) signals: A record of electrical
activity of the heart
▪ Electroencephalogram (EEG) signals: A record of fluctuations
in the electrical activity of large groups of neurons in the
brain
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Lec. 1: Intro.
EECE233: Signals and Systems
Analog vs. Digital Signal Processing
• Analog signal processing
▪ Continuous-time signals
▪ Solve differential equations in real time
▪ Analog circuit elements: Resistors, capacitors, inductors,
transistor amplifiers
• Digital signal processing
▪ Discrete-time signals: Discrete only in time
▪ Digital signals: Discrete both in time and amplitude
▪ Flexibility: Software (program)-oriented (e.g., DSP)
▪ Repeatability
▪ VLSI circuits on silicon chips, causing a low cost
▪ Near real time
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Lec. 1: Intro.
EECE233: Signals and Systems
Applications of Signals and Systems
• All areas of electrical engineering
▪ Sensor application
• Detection, estimation, tracking, radar signal processing, sonar
signal processing, acoustic signal processing
▪ Communication
• Cellular networks (5G), wireless LANs (Wi-Fi), Bluetooth,
satellite communications (Starlink)
▪ Image processing
• Pattern recognition, machine learning, image denoising, Deep
learning, data compression (jpg)
▪ Speech
• Speech recognition, speech synthesis, digital audio, adaptive
noise cancellation
▪ Biomedical applications
• Biomedical imaging (CT, MRI), ECG (electrocardiogram) and EEG
(electroencephalogram) analysis
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Lec. 1: Intro.
EECE233: Signals and Systems
Contents
• Introduction to Signals and Systems
• Classification of Signals
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Lec. 1: Intro.
EECE233: Signals and Systems
Representation of Complex Numbers
• Cartesian form:
• Polar form:
• Relationships:
• Euler’s formula:
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EECE233: Signals and Systems
Classification of Signals
• Real-valued signals vs. complex-valued signals
• Continuous-time signals vs. discrete-time signals
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EECE233: Signals and Systems
Classification of Signals
• Even signals vs. odd signals
▪ Even signal:
▪ Odd signal:
• An arbitrary signal 𝑥 𝑡 can be decomposed into its even
part and odd part
Communication
with bit errors
Communication
with bit errors
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Lec. 1: Intro.
EECE233: Signals and Systems
Classification of Signals
• In the case of complex-valued signals, conjugate
symmetric if
▪ If 𝑥 𝑡 has a conjugate symmetry, then its real part is even
and its imaginary part is odd
▪ In addition, its magnitude is even and its phase is odd
Communication
with bit errors
Communication
with bit errors
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Lec. 1: Intro.
EECE233: Signals and Systems
Classification of Signals
• Periodic signals vs. nonperiodic signals
• In the case of continuous-time signals, periodic signal if
▪ Fundamental period: The smallest value of periods, 𝑇0
▪ Fundamental frequency:
▪ Fundamental radian (angular) frequency:
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Lec. 1: Intro.
EECE233: Signals and Systems
Classification of Signals
• In the case of discrete-time signals, periodic signal if
▪ Fundamental period: 𝑁0
▪ Fundamental radian (angular) frequency:
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EECE233: Signals and Systems
Classification of Signals
• Energy signals vs. power signals
• The instantaneous power of the signal:
• Total energy of the continuous-time signal:
• Average power of the continuous-time and non-periodic
signal:
• Average power of the continuous-time and periodic signal
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Lec. 1: Intro.
EECE233: Signals and Systems
Classification of Signals
• Energy of the discrete-time signal:
• Average power of the discrete-time and nonperiodic signal:
• Power of the discrete-time and periodic signal:
• Energy signal iff 0 < 𝐸 < ∞
▪ Energy signal has zero average power
▪ Deterministic and nonperiodic signals
• Power signal iff 0 < 𝑃 < ∞
▪ Power signal has infinite energy
▪ Random and periodic signals
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Lec. 1: Intro.
EECE233: Signals and Systems
Classification of Signals
• Deterministic signals vs. random signals
• Deterministic signals
▪ A signal about which there is no uncertainty with respect to
its value at any time
• Random signals
▪ A signal about which there is uncertainty before it occurs
▪ Belongs to an ensemble (group of signals)
▪ Each signal within the ensemble has a certain probability of
occurrence
▪ All signals that can be measured in the world are random
signals due to noises (thermal noise, electrical noise, etc.)
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