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