<< Chapter < Page Chapter >> Page >
Describes various classifications of systems.


In this module some of the basic classifications of systems will be briefly introduced and the most important propertiesof these systems are explained. As can be seen, the properties of a system provide an easy way to distinguish onesystem from another. Understanding these basic differences between systems, and their properties, will be a fundamentalconcept used in all signal and system courses. Once a set of systems can be identified as sharing particular properties, one no longer hasto reprove a certain characteristic of a system each time, but it can simply be known due to the the systemclassification.

Classification of systems

Continuous vs. discrete

One of the most important distinctions to understand is the difference between discrete time and continuous time systems. A system in which the input signal and output signal both have continuous domains is said to be a continuous system. One in which the input signal and output signal both have discrete domains is said to be a discrete system. Of course, it is possible to conceive of signals that belong to neither category, such as systems in which sampling of a continuous time signal or reconstruction from a discrete time signal take place.

Linear vs. nonlinear

A linear system is any system that obeys the properties of scaling (first order homogeneity) and superposition (additivity) further described below. A nonlinear system is any system that does not have at least one of these properties.

To show that a system H obeys the scaling property is to show that

H k f t k H f t

A block diagram demonstrating the scaling property of linearity

To demonstrate that a system H obeys thesuperposition property of linearity is to show that

H f 1 t f 2 t H f 1 t H f 2 t

A block diagram demonstrating the superposition property oflinearity

It is possible to check a system for linearity in a single (though larger) step. To do this, simply combine the firsttwo steps to get

H k 1 f 1 t k 2 f 2 t k 1 H f 1 t k 2 H f 2 t

Time invariant vs. time varying

A system is said to be time invariant if it commutes with the parameter shift operator defined by S T ( f ( t ) ) = f ( t - T ) for all T , which is to say

H S T = S T H

for all real T . Intuitively, that means that for any input function that produces some output function, any time shift of that input function will produce an output function identical in every way except that it is shifted by the same amount. Any system that does not have this property is said to be time varying.

This block diagram shows what the condition for time invariance. The output is the same whether the delay is puton the input or the output.

Causal vs. noncausal

A causal system is one in which the output depends only on current or past inputs, but not future inputs. Similarly, an anticausal system is one in which the output depends only on current or future inputs, but not past inputs. Finally, a noncausal system is one in which the output depends on both past and future inputs. All "realtime" systems must be causal, since they can not have future inputs available to them.

One may think the idea of future inputs does not seem to make much physical sense; however, we have only beendealing with time as our dependent variable so far, which is not always the case. Imagine rather that we wanted to doimage processing. Then the dependent variable might represent pixel positions to the left and right (the "future") of the currentposition on the image, and we would not necessarily have a causal system.

For a typical system to be causal...
...the output at time t 0 , y t 0 , can only depend on the portion of the input signal before t 0 .

Stable vs. unstable

There are several definitions of stability, but the one that will be used most frequently in this course will be bounded input, bounded output (BIBO) stability. In this context, a stable system is one in which the output is bounded if the input is also bounded. Similarly, an unstable system is one in which at least one bounded input produces an unbounded output.

Representing this mathematically, a stable system must have the following property, where x t is the input and y t is the output. The output must satisfy the condition

y t M y
whenever we have an input to the system that satisfies
x t M x
M x and M y both represent a set of finite positive numbers and these relationships hold for all of t . Otherwise, the system is unstable.

System classifications summary

This module describes just some of the many ways in which systems can be classified. Systems can be continuous time, discrete time, or neither. They can be linear or nonlinear, time invariant or time varying, and stable or unstable. We can also divide them based on their causality properties. There are other ways to classify systems, such as use of memory, that are not discussed here but will be described in subsequent modules.

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Signals and systems' conversation and receive update notifications?