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Introduction to the Signals chapter

To describe signals and to understand that signals can carry information we need tools for mathematical description and manipulation of signals.

In this chapter we introduce several important signals and show simple methods of describing them. Depending on which type of signals we are looking at, it will bedifferent methods availiable for manipulating them. The elementary operations for manipulating signals and sequences will be described.

    Contents of this chapter

  • Introduction (current module)
  • Discrete time signals
  • Analog signals
  • Discrete vs Analog signals
  • Frequency definitions and periodicity
  • Energy&Power
  • Exercises

The simplest signals are one-dimensional and what follows is a classification of them.

Classification of signals

Analog signals

An analog signal is a continuous function of a continuous variable. Referring to , this corresponds to that both the 1st AND the 2nd axis is continuous. The 1st axiswill in general correspond to the variable t , meaning time. In this context we define

  • signal range - the possible amplitude values the signal can take
  • signal axis - the time interval for which the signal exists
Reference axes

Time discrete signals

A time discrete signal is a continuous signal of a discrete variable. Referring to , we have the 1st axis discrete while the 2nd axis is continuous. Often we assign the values of the 1st axis to a variable n . Time discrete signals often originate from analog signals being sampled.More on that in the Sampling theorem chapter.

Time discrete signal
Note that the signal is only defined for integer values along the 1st axis. We do not have any information other than the values at index points.

Digital signals

Let the signal be a discrete function of a discrete variable, e.g. 1st and 2nd axis discrete, then the signal will be digital . Examples of digital signals are a binary sequence. Digital signals often arise from samplinganalog signals and the samples being assigned to a discrete value.

Periodic vs non periodic signals

All the signals mentioned above can be periodic. For time discrete and digital signals one has to be extra cautious when "declaring" periodicity as wewill see in Frequency definitions&periodicity . shows a periodic signal with period T 0 and an aperiodic signal.

Periodic signal
Aperiodic signal
(Figures by Melissa Selik)

Matlab file


Take a look at

  • Discrete time signals
  • Analog signals
  • Discrete vs Analog signals
  • Frequency definitions and periodicity
  • Energy&Power
  • Exercises

Questions & Answers

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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
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anyone know any internet site where one can find nanotechnology papers?
Damian Reply
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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.
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Damian Reply
absolutely yes
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s. Reply
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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?
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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.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19
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