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.
v (t )  Ri (t )
• Examples:
– Circuits (Input: Voltage, Output: Current)
• Simple resistor circuit:
– Mass Spring System (Input: Force, Output: displacement)
– Automatic Speaker Recognition (Input: Speech, Output: Identity)
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
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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onedimensional
• 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.:
x[n]  x(nTs ), Ts
September 2, 2009
is
sampling
ECE 366, Fall 2009
period
• 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
x (t )  x (t  T )
– The smallest T, that satisfies this relationship is called
the fundamental period.
1
f

–
T is called the frequency of the signal (Hz).
– Angular frequency,  2f  2T
(radians/sec).
– A signal is either periodic or aperiodic.
– A periodic signal must continue forever.
– Example: The voltage at an AC
power source
is
a T
b T
periodic.

September 2, 2009
a
ECE 366, Fall 2009
0
x(t )dt 
0
 x(t )dt   x(t )dt
b
T0
• 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.
x (t )  x ( t )
2
x (t )  x ( t )
xo (t ) 
2
xe (t ) 
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
a
a
 x (t )dt  2 x (t )dt
e
a
0
a
x
o
a
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ECE 366, Fall 2009
e
(t )dt  0
• 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.
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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).
 x (t )dt
– Total Energy: lim
– Average Power: lim T1  x (t )dt
T /2
2
T 
T / 2
T /2
2
T 
T / 2
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.
September 2, 2009
ECE 366, Fall 2009