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September 2, 2009 ECE 366, Fall 2009
Introduction to ECE 366
Selin Aviyente
Associate Professor
September 2, 2009 ECE 366, Fall 2009
Overview
• Lectures: M,W,F 8:00-8:50 a.m.,
1257 Anthony Hall
• Web Page:
http://www.egr.msu.edu/~aviyente/ece366_09
• Textbook: Linear Systems and Signals, Lathi ,
2nd Edition, Oxford Press.
• Office Hours: M,W 3:00-4:30 p.m., 2210
Engineering Building
• Pre-requisites: ECE 202, 280
September 2, 2009 ECE 366, Fall 2009
Course Requirements
• 2 Midterm Exams-40%
– October 16th
– November 20th
• Weekly HW Assignments-10%
– Assigned Friday due next Friday (except during exam
weeks)
– Will include MATLAB assignments.
– Should be your own work.
– No late HWs will be accepted.
– Lowest HW grade is dropped.
• Final Project-15% (MATLAB based project)
• Final Exam-35%, December 15th
September 2, 2009 ECE 366, Fall 2009
Policies
• Cheating in any form will not be tolerated.
This includes copying HWs, cheating on
exams.
• You are allowed to discuss the HW
questions with your friends, and me.
• However, you have to write up the
homework solutions on your own.
• Lowest HW grade will be dropped.
September 2, 2009 ECE 366, Fall 2009
Course Outline
• Part 1- Continuous Time Signals and
Systems
– Basic Signals and Systems Concepts
– Time Domain Analysis of Linear Time
Invariant (LTI) Systems
– Frequency Domain Analysis of Signals and
Systems
• Fourier Series
• Fourier Transform
• Applications
September 2, 2009 ECE 366, Fall 2009
Course Outline
• Part 2- Discrete Time Signals and
Systems
– Basic DT Signals and Systems Concepts
– Time Domain Analysis of DT Systems
– Frequency Domain Analysis of DT Signals
and Systems
• Z-transforms
• DTFT
September 2, 2009 ECE 366, Fall 2009
Signals
• A signal is a function of one or more variables that
conveys information about a physical phenomenon.
• Signals are functions of independent variables; time (t)
or space (x,y)
• A physical signal is modeled using mathematical
functions.
• Examples:
– Electrical signals: Voltages/currents in a circuit v(t),i(t)
– Temperature (may vary with time/space)
– Acoustic signals: audio/speech signals (varies with time)
– Video (varies with time and space)
– Biological signals: Heartbeat, EEG
September 2, 2009 ECE 366, Fall 2009
Systems
• A system is an entity that manipulates one or more
signals that accomplish a function, thereby yielding new
signals.
• The input/output relationship of a system is modeled
using mathematical equations.
• We want to study the response of systems to signals.
• A system may be made up of physical components
(electrical, mechanical, hydraulic) or may be an
algorithm that computes an output from an input signal.
• Examples:
– Circuits (Input: Voltage, Output: Current)
• Simple resistor circuit:
– Mass Spring System (Input: Force, Output: displacement)
– Automatic Speaker Recognition (Input: Speech, Output: Identity)
)
(
)
( t
Ri
t
v 
September 2, 2009 ECE 366, Fall 2009
Applications of Signals and
Systems
• Acoustics: Restore speech in a noisy environment such
as cockpit
• Communications: Transmission in mobile phones, GPS,
radar and sonar
• Multimedia: Compress signals to store data such as
CDs, DVDs
• Biomedical: Extract information from biological signals:
– Electrocardiogram (ECG) electrical signals generated by the
heart
– Electroencephalogram (EEG) electrical signals generated by the
brain
– Medical Imaging
• Biometrics: Fingerprint identification, speaker
recognition, iris recognition
September 2, 2009 ECE 366, Fall 2009
Classification of Signals
• One-dimensional vs. Multi-dimensional:
The signal can be a function of a single
variable or multiple variables.
– Examples:
• Speech varies as a function of timeone-
dimensional
• Image intensity varies as a function of (x,y)
coordinatesmulti-dimensional
– In this course, we focus on one-dimensional
signals.
September 2, 2009 ECE 366, Fall 2009
• Continuous-time vs. discrete-time:
– A signal is continuous time if it is defined for
all time, x(t).
– A signal is discrete time if it is defined only at
discrete instants of time, x[n].
– A discrete time signal is derived from a
continuous time signal through sampling, i.e.:
period
sampling
is
T
nT
x
n
x s
s ),
(
]
[ 
September 2, 2009 ECE 366, Fall 2009
• Analog vs. Digital:
– A signal whose amplitude can take on any
value in a continuous range is an analog
signal.
– A digital signal is one whose amplitude can
take on only a finite number of values.
– Example: Binary signals are digital signals.
– An analog signal can be converted into a
digital signal through quantization.
September 2, 2009 ECE 366, Fall 2009
• Deterministic vs. Random:
– A signal is deterministic if we can define its
value at each time point as a mathematical
function
– A signal is random if it cannot be described by
a mathematical function (can only define
statistics)
– Example:
• Electrical noise generated in an amplifier of a
radio/TV receiver.
September 2, 2009 ECE 366, Fall 2009
• Periodic vs. Aperiodic Signals:
– A periodic signal x(t) is a function of time that satisfies
– The smallest T, that satisfies this relationship is called
the fundamental period.
– is called the frequency of the signal (Hz).
– Angular frequency, (radians/sec).
– A signal is either periodic or aperiodic.
– A periodic signal must continue forever.
– Example: The voltage at an AC power source is
periodic.
)
(
)
( T
t
x
t
x 

T
f
1

  
 


0 0
0
)
(
)
(
)
(
T
a
a
T
b
b T
dt
t
x
dt
t
x
dt
t
x
T
f



2
2 

September 2, 2009 ECE 366, Fall 2009
• Causal, Anticausal vs. Noncausal Signals:
– A signal that does not start before t=0 is a
causal signal. x(t)=0, t<0
– A signal that starts before t=0 is a noncausal
signal.
– A signal that is zero for t>0 is called an
anticausal signal.
September 2, 2009 ECE 366, Fall 2009
• Even vs. Odd:
– A signal is even if x(t)=x(-t).
– A signal is odd if x(t)=-x(-t)
– Examples:
• Sin(t) is an odd signal.
• Cos(t) is an even signal.
– A signal can be even, odd or neither.
– Any signal can be written as a combination of
an even and odd signal.
2
)
(
)
(
)
(
2
)
(
)
(
)
(
t
x
t
x
t
x
t
x
t
x
t
x
o
e






September 2, 2009 ECE 366, Fall 2009
Properties of Even and Odd
Functions
• Even x Odd = Odd
• Odd x Odd = Even
• Even x Even = Even
• Even + Even = Even
• Even + Odd = Neither
• Odd + Odd = Odd
0
)
(
)
(
2
)
(
0







dt
t
x
dt
t
x
dt
t
x
a
a
o
a
e
a
a
e
September 2, 2009 ECE 366, Fall 2009
• Finite vs. Infinite Length:
– X(t) is a finite length signal if it is nonzero over
a finite interval a<t<b
– X(t) is infinite length signal if it is nonzero over
all real numbers.
– Periodic signals are infinite length.
September 2, 2009 ECE 366, Fall 2009
• Energy signals vs. power signals:
– Consider a voltage v(t) developed across a
resistor R, producing a current i(t).
– The instantaneous power: p(t)=v2(t)/R=Ri2(t)
– In signal analysis, the instantaneous power of
a signal x(t) is equivalent to the instantaneous
power over 1 resistor and is defined as x2(t).
– Total Energy:
– Average Power: 



2
/
2
/
2
)
(
1
lim
T
T
T dt
t
x
T




2
/
2
/
2
)
(
lim
T
T
T dt
t
x
September 2, 2009 ECE 366, Fall 2009
• Energy vs. Power Signals:
– A signal is an energy signal if its energy is finite,
0<E<∞.
– A signal is a power signal if its power is finite, 0<P<∞.
– An energy signal has zero power, and a power signal
has infinite energy.
– Periodic signals and random signals are usually
power signals.
– Signals that are both deterministic and aperiodic are
usually energy signals.
– Finite length and finite amplitude signals are energy
signals.

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ece366_intro ECE.ppt Modulation Demodu

  • 1. September 2, 2009 ECE 366, Fall 2009 Introduction to ECE 366 Selin Aviyente Associate Professor
  • 2. September 2, 2009 ECE 366, Fall 2009 Overview • Lectures: M,W,F 8:00-8:50 a.m., 1257 Anthony Hall • Web Page: http://www.egr.msu.edu/~aviyente/ece366_09 • Textbook: Linear Systems and Signals, Lathi , 2nd Edition, Oxford Press. • Office Hours: M,W 3:00-4:30 p.m., 2210 Engineering Building • Pre-requisites: ECE 202, 280
  • 3. September 2, 2009 ECE 366, Fall 2009 Course Requirements • 2 Midterm Exams-40% – October 16th – November 20th • Weekly HW Assignments-10% – Assigned Friday due next Friday (except during exam weeks) – Will include MATLAB assignments. – Should be your own work. – No late HWs will be accepted. – Lowest HW grade is dropped. • Final Project-15% (MATLAB based project) • Final Exam-35%, December 15th
  • 4. September 2, 2009 ECE 366, Fall 2009 Policies • Cheating in any form will not be tolerated. This includes copying HWs, cheating on exams. • You are allowed to discuss the HW questions with your friends, and me. • However, you have to write up the homework solutions on your own. • Lowest HW grade will be dropped.
  • 5. September 2, 2009 ECE 366, Fall 2009 Course Outline • Part 1- Continuous Time Signals and Systems – Basic Signals and Systems Concepts – Time Domain Analysis of Linear Time Invariant (LTI) Systems – Frequency Domain Analysis of Signals and Systems • Fourier Series • Fourier Transform • Applications
  • 6. September 2, 2009 ECE 366, Fall 2009 Course Outline • Part 2- Discrete Time Signals and Systems – Basic DT Signals and Systems Concepts – Time Domain Analysis of DT Systems – Frequency Domain Analysis of DT Signals and Systems • Z-transforms • DTFT
  • 7. September 2, 2009 ECE 366, Fall 2009 Signals • A signal is a function of one or more variables that conveys information about a physical phenomenon. • Signals are functions of independent variables; time (t) or space (x,y) • A physical signal is modeled using mathematical functions. • Examples: – Electrical signals: Voltages/currents in a circuit v(t),i(t) – Temperature (may vary with time/space) – Acoustic signals: audio/speech signals (varies with time) – Video (varies with time and space) – Biological signals: Heartbeat, EEG
  • 8. September 2, 2009 ECE 366, Fall 2009 Systems • A system is an entity that manipulates one or more signals that accomplish a function, thereby yielding new signals. • The input/output relationship of a system is modeled using mathematical equations. • We want to study the response of systems to signals. • A system may be made up of physical components (electrical, mechanical, hydraulic) or may be an algorithm that computes an output from an input signal. • Examples: – Circuits (Input: Voltage, Output: Current) • Simple resistor circuit: – Mass Spring System (Input: Force, Output: displacement) – Automatic Speaker Recognition (Input: Speech, Output: Identity) ) ( ) ( t Ri t v 
  • 9. September 2, 2009 ECE 366, Fall 2009 Applications of Signals and Systems • Acoustics: Restore speech in a noisy environment such as cockpit • Communications: Transmission in mobile phones, GPS, radar and sonar • Multimedia: Compress signals to store data such as CDs, DVDs • Biomedical: Extract information from biological signals: – Electrocardiogram (ECG) electrical signals generated by the heart – Electroencephalogram (EEG) electrical signals generated by the brain – Medical Imaging • Biometrics: Fingerprint identification, speaker recognition, iris recognition
  • 10. September 2, 2009 ECE 366, Fall 2009 Classification of Signals • One-dimensional vs. Multi-dimensional: The signal can be a function of a single variable or multiple variables. – Examples: • Speech varies as a function of timeone- dimensional • Image intensity varies as a function of (x,y) coordinatesmulti-dimensional – In this course, we focus on one-dimensional signals.
  • 11. September 2, 2009 ECE 366, Fall 2009 • Continuous-time vs. discrete-time: – A signal is continuous time if it is defined for all time, x(t). – A signal is discrete time if it is defined only at discrete instants of time, x[n]. – A discrete time signal is derived from a continuous time signal through sampling, i.e.: period sampling is T nT x n x s s ), ( ] [ 
  • 12. September 2, 2009 ECE 366, Fall 2009 • Analog vs. Digital: – A signal whose amplitude can take on any value in a continuous range is an analog signal. – A digital signal is one whose amplitude can take on only a finite number of values. – Example: Binary signals are digital signals. – An analog signal can be converted into a digital signal through quantization.
  • 13. September 2, 2009 ECE 366, Fall 2009 • Deterministic vs. Random: – A signal is deterministic if we can define its value at each time point as a mathematical function – A signal is random if it cannot be described by a mathematical function (can only define statistics) – Example: • Electrical noise generated in an amplifier of a radio/TV receiver.
  • 14. September 2, 2009 ECE 366, Fall 2009 • Periodic vs. Aperiodic Signals: – A periodic signal x(t) is a function of time that satisfies – The smallest T, that satisfies this relationship is called the fundamental period. – is called the frequency of the signal (Hz). – Angular frequency, (radians/sec). – A signal is either periodic or aperiodic. – A periodic signal must continue forever. – Example: The voltage at an AC power source is periodic. ) ( ) ( T t x t x   T f 1         0 0 0 ) ( ) ( ) ( T a a T b b T dt t x dt t x dt t x T f    2 2  
  • 15. September 2, 2009 ECE 366, Fall 2009 • Causal, Anticausal vs. Noncausal Signals: – A signal that does not start before t=0 is a causal signal. x(t)=0, t<0 – A signal that starts before t=0 is a noncausal signal. – A signal that is zero for t>0 is called an anticausal signal.
  • 16. September 2, 2009 ECE 366, Fall 2009 • Even vs. Odd: – A signal is even if x(t)=x(-t). – A signal is odd if x(t)=-x(-t) – Examples: • Sin(t) is an odd signal. • Cos(t) is an even signal. – A signal can be even, odd or neither. – Any signal can be written as a combination of an even and odd signal. 2 ) ( ) ( ) ( 2 ) ( ) ( ) ( t x t x t x t x t x t x o e      
  • 17. September 2, 2009 ECE 366, Fall 2009 Properties of Even and Odd Functions • Even x Odd = Odd • Odd x Odd = Even • Even x Even = Even • Even + Even = Even • Even + Odd = Neither • Odd + Odd = Odd 0 ) ( ) ( 2 ) ( 0        dt t x dt t x dt t x a a o a e a a e
  • 18. September 2, 2009 ECE 366, Fall 2009 • Finite vs. Infinite Length: – X(t) is a finite length signal if it is nonzero over a finite interval a<t<b – X(t) is infinite length signal if it is nonzero over all real numbers. – Periodic signals are infinite length.
  • 19. September 2, 2009 ECE 366, Fall 2009 • Energy signals vs. power signals: – Consider a voltage v(t) developed across a resistor R, producing a current i(t). – The instantaneous power: p(t)=v2(t)/R=Ri2(t) – In signal analysis, the instantaneous power of a signal x(t) is equivalent to the instantaneous power over 1 resistor and is defined as x2(t). – Total Energy: – Average Power:     2 / 2 / 2 ) ( 1 lim T T T dt t x T     2 / 2 / 2 ) ( lim T T T dt t x
  • 20. September 2, 2009 ECE 366, Fall 2009 • Energy vs. Power Signals: – A signal is an energy signal if its energy is finite, 0<E<∞. – A signal is a power signal if its power is finite, 0<P<∞. – An energy signal has zero power, and a power signal has infinite energy. – Periodic signals and random signals are usually power signals. – Signals that are both deterministic and aperiodic are usually energy signals. – Finite length and finite amplitude signals are energy signals.