208503 Signals and Systems
Lecture 1: Introduction
Books
Text Book:
Signals, Systems and Transforms (Fourth Edition)
Charles L. Phillips, John M. Parr, Eve A. Riskin
Reference:
Signals and Systems (2nd Edition)
Alan V. Oppenheim, Alan V. Willsky, S.Hamid Nawab
Internet
Grading Policy (Tentative)
OHT
30%
Final
40%
Quiz
15%
Research Report
10%
Signal
• Any physical quantity that
exhibits variation in space or
time
• Describes how one parameter
varies with another parameter
• Conveys information about a
wide
variety
of
physical
phenomena.
• Signals and Systems
Definition
A signal is defined as a real or complex function of some
independent variables that conveys information on the nature of
the physical phenomenon it is representing
Signals can be:
• 1-dimensional or multi-dimensional
• continuous-time (CT) or discrete-time (DT)
• deterministic or stochastic (random, probabilistic)
1 Dimensional vs Multidimensional Signals
ECG signal
2-D image signal
Multidimensional image signal
CT vs DT Signals
Signal representing the speciesabundance
relation
of
an
ecological community
Example of recording of speech signals. The signal represents
acoustic pressure variations against time
Deterministic vs Stochastic Signals
• Signals that can be modeled exactly by a mathematical formula are known
as deterministic signals.
• Deterministic signals are not always adequate to model real-world
situations.
• Random signals, on the other hand, cannot be described by a
mathematical equation; they are modeled in probabilistic terms.
Systems
• A system is an entity that processes signals.
• A system is any process that generates an output signal in
response to an input signal.
• Systems are collections of software or hardware elements,
components, subsystems.
Mathematical Modeling of Signals & Systems
Engineers must model the two distinct phenomena _signals &
systems.
Physical signals are modeled by mathematical functions e.g., for the
circuit shown in figure below v(t) is the voltage signal
Physical systems are modeled by mathematical equations.
For CT systems, linear differential equations with constant coefficients
are used.
For DT systems, linear constant coefficient difference equations are
used.
Scope of the Subject
This subject covers the time and frequency analysis of both
Continuous-Time (CT) and Discrete-Time (DT)signals and systems.
We will start with CT signals and extend the concepts to DT signals.