Signals & System
Lecture 3
Signals Concepts & Properties
Dr. Tahir Zaidi
,Lecture 3: Signals & Systems Concepts
Systems, signals, mathematical models. Continuous-
time and discrete-time signals. Energy and power
signals. Linear systems. Examples for use
throughout the course, introduction to Matlab and
Simulink tools.
Specific objectives:
• Introduction to systems
• Continuous and discrete time systems
• Properties of a system
• Linear (time invariant) LTI systems
• System implementation in Matlab and Simulink
, Lecture 3: Resources
SaS, Oppenheim & Willsky, C1
MIT notes, Lecture 2
Mastering Matlab 6, Prentice Hall
Mastering Simulink 4
Matlab help
, Linear Systems
A system takes a signal as an input and transforms it into
another signal
Linear systems play a crucial role in most areas of science
– Closed form solutions often exist
– Theoretical analysis is considerably simplified
– Non-linear systems can often be regarded as linear, for
small perturbations, so-called linearization
For the remainder of the lecture/course we’re primarily going
to be considering Linear, Time Invariant systems (LTI) and
consider their properties
continuous
x(t) y(t)
time (CT)
discrete
x[n] y[n]
time (DT)
, Examples of Simple Systems
To get some idea of typical systems (and their properties),
consider the electrical circuit example:
dvc (t ) 1 1
vc (t ) vs (t )
dt RC RC
which is a first order, CT differential equation.
Examples of first order, DT difference equations:
y[n] x[n] 1.01y[n 1]
where y is the monthly bank balance, and x is monthly net deposit
RC k
v[n] v[n 1] f [ n]
RC k RC k
which represents a discretised version of the electrical circuit
Example of second order system includes:
d 2 y(t ) dy(t )
a 2
b cy (t ) x(t )
dt dt
System described by order and parameters (a, b, c)
Lecture 3
Signals Concepts & Properties
Dr. Tahir Zaidi
,Lecture 3: Signals & Systems Concepts
Systems, signals, mathematical models. Continuous-
time and discrete-time signals. Energy and power
signals. Linear systems. Examples for use
throughout the course, introduction to Matlab and
Simulink tools.
Specific objectives:
• Introduction to systems
• Continuous and discrete time systems
• Properties of a system
• Linear (time invariant) LTI systems
• System implementation in Matlab and Simulink
, Lecture 3: Resources
SaS, Oppenheim & Willsky, C1
MIT notes, Lecture 2
Mastering Matlab 6, Prentice Hall
Mastering Simulink 4
Matlab help
, Linear Systems
A system takes a signal as an input and transforms it into
another signal
Linear systems play a crucial role in most areas of science
– Closed form solutions often exist
– Theoretical analysis is considerably simplified
– Non-linear systems can often be regarded as linear, for
small perturbations, so-called linearization
For the remainder of the lecture/course we’re primarily going
to be considering Linear, Time Invariant systems (LTI) and
consider their properties
continuous
x(t) y(t)
time (CT)
discrete
x[n] y[n]
time (DT)
, Examples of Simple Systems
To get some idea of typical systems (and their properties),
consider the electrical circuit example:
dvc (t ) 1 1
vc (t ) vs (t )
dt RC RC
which is a first order, CT differential equation.
Examples of first order, DT difference equations:
y[n] x[n] 1.01y[n 1]
where y is the monthly bank balance, and x is monthly net deposit
RC k
v[n] v[n 1] f [ n]
RC k RC k
which represents a discretised version of the electrical circuit
Example of second order system includes:
d 2 y(t ) dy(t )
a 2
b cy (t ) x(t )
dt dt
System described by order and parameters (a, b, c)
