Signals and systems Fall 2003 Lecture #1 Prof Alan S. Willsky 4 September 2003 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
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
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(ega CAT scan) Biological signals ---sequence of bases in a gene
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 • . • . •
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 calltime Continuous-Time(CT)signals: x(o), t-continuous values Discrete-Time (DT) signals: x[], n-integer values only
3 THE INDEPENDENT VARIABLES • Can be continuous — Trajectory of a space shuttle — Mass density in a cross-section of a brain • C a n b e d i s c r e t e — 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
CT Signals X() Most of the signals in the physical world are ct signals--E. g. voltage current, pressure, temperature, velocity, etc
4 CT Signals • Most of the signals in the physical world are CT signals—E.g. voltage & current, pressure, temperature, velocity, etc
DT Signals Inl, n-integer, time varies discretely xIn [o] x-1x1 98715432 -6 101234567 Examples of dt signals in nature dna base sequence Population of the nth generation of certain species
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
Many human-made dt signals Ex#1 Weekly dow-Jones Ex. #2 digital image industrial average 350 300 200 50 0 Jan.5,1929 Jan.4,1930 Courtesy of Jason Oppenheim Used with permission Why dt?- Can be processed by modern digital computers and digital signal processors DSPs
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
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 CT SyStem DT SyStem
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) CT System y(t) x[n] DT System y[n]
EXAMPLES OF SYSTEMS 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
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
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
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 + +