Lecture 8 - Classification of Systems Notes | EduRev

: Lecture 8 - Classification of Systems Notes | EduRev

 Page 1


Module 1 : Signals in Natural Domain
Lecture 8 : Classification of Systems
Objectives
 In this lecture you will learn the following
We shall classify systems under the following categories and tabulate their system properties
Continuous-time systems
Discrete-time systems
Hybrid : Continuous-Discrete systems
Hybrid : Discrete-Continuous systems
Properties of discrete variable systems
We have classified systems into three classes - Continuous-time systems, Discrete-time systems and Hybrid systems. Now that we have
introduced some system properties, let us see what properties are relevant to which classes of systems.
Let us first consider examples of different classes of systems.
Continuous-time systems
Continuous-Continuous systems
1.Tree swaying in the wind:
Wind - described by its speed, direction - is a
continuous-time input.
Movement of branches is continuous-time
output signal.
Discrete-time systems
Discrete-Discrete systems
1.Logic circuits:
Discrete logic inputs are processed to give
discrete logic outputs.
Hybrid systems
Continuous-Discrete systems
1.Eye: sees continuous image, but sends a
discrete map to the brain
2.Computer microphone: Sampler converts a
continuous time signal into a discrete time
signal.(Sampler forms an important system
in today’s digital world - we shall look at this
in great detail later in the course)
Hybrid systems
Discrete-Continuous systems
1.Brain : gets a discrete map from the eye,
and completes a smooth, continuous picture
2.Computer speaker and sound card - a
digital music output given by the computer is
smoothed out and played as a continuous
waveform.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 2


Module 1 : Signals in Natural Domain
Lecture 8 : Classification of Systems
Objectives
 In this lecture you will learn the following
We shall classify systems under the following categories and tabulate their system properties
Continuous-time systems
Discrete-time systems
Hybrid : Continuous-Discrete systems
Hybrid : Discrete-Continuous systems
Properties of discrete variable systems
We have classified systems into three classes - Continuous-time systems, Discrete-time systems and Hybrid systems. Now that we have
introduced some system properties, let us see what properties are relevant to which classes of systems.
Let us first consider examples of different classes of systems.
Continuous-time systems
Continuous-Continuous systems
1.Tree swaying in the wind:
Wind - described by its speed, direction - is a
continuous-time input.
Movement of branches is continuous-time
output signal.
Discrete-time systems
Discrete-Discrete systems
1.Logic circuits:
Discrete logic inputs are processed to give
discrete logic outputs.
Hybrid systems
Continuous-Discrete systems
1.Eye: sees continuous image, but sends a
discrete map to the brain
2.Computer microphone: Sampler converts a
continuous time signal into a discrete time
signal.(Sampler forms an important system
in today’s digital world - we shall look at this
in great detail later in the course)
Hybrid systems
Discrete-Continuous systems
1.Brain : gets a discrete map from the eye,
and completes a smooth, continuous picture
2.Computer speaker and sound card - a
digital music output given by the computer is
smoothed out and played as a continuous
waveform.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Properties of systems
In early parts of this course, we shall concern ourselves with mainly the first two classes, viz. Continuous-time and Discrete-time
systems, but later we shall also deal with Hybrid systems as well. So, we find it worthwhile here to take a look at what properties the
systems of various classes can have:
 
Property Continuous input -
Continuous output
Discrete input-
Discrete output
Continuous- Discrete input/
Discrete- Continuous output
Memory Yes
If input and output are
of the same type
Yes
If input and output are of
the same type
No
However, we can define a
restricted version of memory if
there is a correspondence in the
input and output variables (e.g.:
continuous and discrete time)
Causality Yes
If input and output are
of the same type
Yes
If input and output are of
the same type
No
A restricted version of causality
can be defined: “If the inputs
are same upto an instant
corresponding to a discrete
variable, then the outputs of a
causal system are same
Shift invariance
(Time
invariance)
Yes
If input and output are
of the same type
Yes
If input and output are of
the same type
No
We can define shift invariance in
cases where the inputs are
shifted by certain quanta
corresponding to the spacing in
discrete variables.
Stability Yes Yes Yes
Linearity Yes Yes Yes
Note that this is a table of properties which the system can have; they are not necessary properties of a system. Hence, we can find a
Continuous-time system that is stable (though there may be Continuous-time systems which are unstable), but it is impossible to apply
the concept of memory to a discrete-continuous system without modifying the concept itself.
 
Conclusion:
In this lecture you have learnt:
Memory, causality and shift invariance are defined only if the input and ouput signals are of the same type i.e. both continuous or
discrete.
Stability and linearity do not require the input and output signals to be of the same type.
Congratulations, you have finished Lecture 8.
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