This document provides an introduction to the ECE 366 Signals and Systems course taught in fall 2009. It outlines the course details such as lectures, textbook, assignments, exams. It also covers an overview of key concepts in signals and systems including definitions of signals, systems, their properties and classifications. Examples of applications are also discussed.

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.
)
(
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( 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.
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t
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t
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t
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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
)
(
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2
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0

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
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t
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t
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a
a
o
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e
a
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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.