1
1) Administrative details
2) Signals
3) Systems
4) For examples,..
“Figures and images used in these lecture notes by permission,
copyright 1997 by Alan V,Oppenheim and Alan S,Willsky”
Signals and Systems
Fall 2003
Lecture #1
Prof,Alan S,Willsky
4 September 2003
2
SIGNALS
Signals are functions of independent variables that carry
information,For example:
Electrical signals --- voltages and currents in a circuit
Acoustic signals --- audio or speech signals (analog or
digital)
Video signals --- intensity variations in an image (e.g,a
CAT scan)
Biological signals --- sequence of bases in a gene
.
.
.
3
THE INDEPENDENT VARIABLES
Can be continuous
— Trajectory of a space shuttle
— Mass density in a cross-section of a brain
Can be discrete
— DNA base sequence
— Digital image pixels
Can be 1-D,2-D, N-D
For this course,Focus on a single (1-D) independent variable
which we call,time”,
Continuous-Time (CT) signals,x(t),t — continuous values
Discrete-Time (DT) signals,x[n],n — integer values only
4
CT Signals
Most of the signals in the physical world are CT
signals—E.g,voltage & current,pressure,
temperature,velocity,etc.
5
DT Signals
Examples of DT signals in nature:
— DNA base sequence
— Population of the nth generation of certain
species
x[n],n — integer,time varies discretely
6
Many human-made DT Signals
Ex.#1 Weekly Dow-Jones
industrial average
Why DT? — Can be processed by modern digital computers
and digital signal processors (DSPs).
Ex.#2 digital image
Courtesy of Jason Oppenheim.
Used with permission.
7
SYSTEMS
For the most part,our view of systems will be from an
input-output perspective:
A system responds to applied input signals,and its response
is described in terms of one or more output signals
x(t) y(t)
CT System
DT System
x[n]
y[n]
8
An RLC circuit
Dynamics of an aircraft or space vehicle
An algorithm for analyzing financial and economic
factors to predict bond prices
An algorithm for post-flight analysis of a space launch
An edge detection algorithm for medical images
EXAMPLES OF SYSTEMS
9
SYSTEM INTERCONNECTIOINS
An important concept is that of interconnecting systems
— To build more complex systems by interconnecting
simpler subsystems
— To modify response of a system
Signal flow (Block) diagram
Cascade
Feedback
Parallel
+
+
1) Administrative details
2) Signals
3) Systems
4) For examples,..
“Figures and images used in these lecture notes by permission,
copyright 1997 by Alan V,Oppenheim and Alan S,Willsky”
Signals and Systems
Fall 2003
Lecture #1
Prof,Alan S,Willsky
4 September 2003
2
SIGNALS
Signals are functions of independent variables that carry
information,For example:
Electrical signals --- voltages and currents in a circuit
Acoustic signals --- audio or speech signals (analog or
digital)
Video signals --- intensity variations in an image (e.g,a
CAT scan)
Biological signals --- sequence of bases in a gene
.
.
.
3
THE INDEPENDENT VARIABLES
Can be continuous
— Trajectory of a space shuttle
— Mass density in a cross-section of a brain
Can be discrete
— DNA base sequence
— Digital image pixels
Can be 1-D,2-D, N-D
For this course,Focus on a single (1-D) independent variable
which we call,time”,
Continuous-Time (CT) signals,x(t),t — continuous values
Discrete-Time (DT) signals,x[n],n — integer values only
4
CT Signals
Most of the signals in the physical world are CT
signals—E.g,voltage & current,pressure,
temperature,velocity,etc.
5
DT Signals
Examples of DT signals in nature:
— DNA base sequence
— Population of the nth generation of certain
species
x[n],n — integer,time varies discretely
6
Many human-made DT Signals
Ex.#1 Weekly Dow-Jones
industrial average
Why DT? — Can be processed by modern digital computers
and digital signal processors (DSPs).
Ex.#2 digital image
Courtesy of Jason Oppenheim.
Used with permission.
7
SYSTEMS
For the most part,our view of systems will be from an
input-output perspective:
A system responds to applied input signals,and its response
is described in terms of one or more output signals
x(t) y(t)
CT System
DT System
x[n]
y[n]
8
An RLC circuit
Dynamics of an aircraft or space vehicle
An algorithm for analyzing financial and economic
factors to predict bond prices
An algorithm for post-flight analysis of a space launch
An edge detection algorithm for medical images
EXAMPLES OF SYSTEMS
9
SYSTEM INTERCONNECTIOINS
An important concept is that of interconnecting systems
— To build more complex systems by interconnecting
simpler subsystems
— To modify response of a system
Signal flow (Block) diagram
Cascade
Feedback
Parallel
+
+
