View source for Signal

{{short description|Varying physical quantity that conveys information}}
{{other uses}}
{{Use American English|date=June 2019}}

[[File:William Powell Frith The signal 1858.jpg|thumb|right|In ''The Signal'' by [[William Powell Frith]], a woman sends a signal by waving a white handkerchief.]]

'''Signal''' refers to both the process and the result of [[Signal transmission|transmission]] of [[data]] over some [[transmission media|media]] accomplished by embedding some variation. Signals are important in multiple subject fields including [[signal processing]], [[information theory]] and [[biology]]. 

In signal processing, a signal is a function that conveys [[information]] about a phenomenon.<ref name=Priemer/> Any quantity that can vary over space or time can be used as a signal to share messages between observers.<ref name=PC/> The ''[[IEEE Transactions on Signal Processing]]'' includes [[audio signal|audio]], [[video]], speech, [[image]], [[sonar]], and [[radar]] as examples of signals.<ref name="IEEE" /> A signal may also be defined as {{em|any}} observable change in a quantity over space or time (a [[time series]]), even if it does not carry information.{{efn|Some authors do not emphasize the role of information in the definition of a signal.<ref name=Sinha/>}}

In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with [[cell signaling]]. [[Signaling theory]], in [[evolutionary biology]], proposes that a substantial driver for [[evolution]] is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically provided by a [[sensor]], and often the original form of a signal is converted to another form of energy using a [[transducer]]. For example, a [[microphone]] converts an acoustic signal to a voltage waveform, and a [[Loudspeaker|speaker]] does the reverse.<ref name="Priemer" />

Another important property of a signal is its [[Entropy (information theory)|entropy]] or [[information content]]. [[Information theory]] serves as the formal study of signals and their content. The information of a signal is often accompanied by [[Noise (electronics)|noise]], which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals ([[crosstalk]]). The reduction of noise is covered in part under the heading of [[signal integrity]]. The separation of desired signals from background noise is the field of [[signal recovery]],<ref name="Wilmshurst" /> one branch of which is [[estimation theory]], a probabilistic approach to suppressing random disturbances.

Engineering disciplines such as electrical engineering have advanced the design, study, and implementation of systems involving [[Data transmission|transmission]], [[data storage device|storage]], and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines: [[electronic engineering]] and [[computer engineering]] developed to specialize in the design and analysis of systems that manipulate physical signals, while [[Industrial design|design engineering]] developed to address the functional design of signals in [[User interface|user–machine interfaces]].

==Definitions==
Definitions specific to sub-fields are common: 
* In [[electronics]] and [[telecommunications]], ''signal'' refers to any time-varying [[voltage]], [[electric current|current]], or [[electromagnetic wave]] that carries information.
* In [[signal processing]], signals are analog and digital representations of analog physical quantities. 
* In [[information theory]], a signal is a codified message, that is, the sequence of [[state variable|states]] in a [[communication channel]] that encodes a message. 
* In a communication system, a ''transmitter'' encodes a ''message'' to create a signal, which is carried to a ''receiver'' by the communication channel.  For example, the words "[[Mary had a little lamb]]" might be the message spoken into a [[telephone]]. The telephone transmitter converts the sounds into an electrical signal. The signal is transmitted to the receiving telephone by wires; at the receiver it is reconverted into sounds.
* In telephone networks, [[Signaling (telecommunications)|signaling]], for example [[common-channel signaling]], refers to phone number and other digital control information rather than the actual voice signal.

== Classification ==
Signals can be categorized in various ways.  The most common{{verify source|date=March 2022}} distinction is between discrete and continuous spaces that the functions are defined over, for example, discrete and continuous-time domains.  [[Discrete-time signal]]s are often referred to as ''[[time series]]'' in other fields.  [[Continuous-time signal]]s are often referred to as ''continuous signals''.

A second important distinction is between discrete-valued and continuous-valued.  Particularly in [[digital signal processing]], a [[Digital signal (signal processing)|digital signal]] may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In [[digital electronics]], digital signals are the continuous-time waveform signals in a digital system, representing a bit-stream.

Signals may also be categorized by their spatial distributions as either point source signals (PSSs) or distributed source signals (DSSs).<ref name=PC/>


In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into [[analog signal]]s and [[digital signal]]s; according to the determinacy of signals, classified into deterministic signals and random signals; according to the [[Signal strength in telecommunications|strength of signals]], classified into energy signals and power signals.

=== Analog and digital signals ===
[[File:Digital-signal-noise.svg|thumb|A digital signal has two or more distinguishable waveforms, in this example, high voltage and low voltages, each of which can be mapped onto a digit. Characteristically, noise can be removed from digital signals provided it is not too extreme.]]

Two main types of signals encountered in practice are ''[[analog signal|analog]]'' and ''[[digital signal|digital]]''. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants.  Digital signals are ''[[Quantization (signal processing)|quantized]]'', while analog signals are continuous.

====Analog signal====
{{main|Analog signal}}

An analog signal  is any [[continuous signal]] for which the time-varying feature of the signal is a representation of some other time varying quantity, i.e., ''analogous'' to another time varying signal.   For example, in an analog [[audio signal]], the instantaneous [[voltage]] of the signal varies continuously with the [[sound pressure]]. It differs from a [[Digital signal (signal processing)|digital signal]], in which the continuous quantity is a representation of a sequence of [[discrete value]]s which can only take on one of a finite number of values.<ref>{{Cite web|url=https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/digital/digital.htm|title=Digital signals|website=www.st-andrews.ac.uk|access-date=2017-12-17|url-status=live|archive-url=https://web.archive.org/web/20170302055200/http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/digital/digital.htm|archive-date=2017-03-02}}</ref><ref>{{Cite web|url=https://learn.sparkfun.com/tutorials/analog-vs-digital/digital-signals|title=Analog vs. Digital - learn.sparkfun.com|website=learn.sparkfun.com|language=en|access-date=2017-12-17|url-status=live|archive-url=https://web.archive.org/web/20170705100418/https://learn.sparkfun.com/tutorials/analog-vs-digital/digital-signals|archive-date=2017-07-05}}</ref>

The term ''analog signal'' usually refers to [[electrical signal]]s; however, analog signals may use other mediums such as [[Classical mechanics|mechanical]], [[pneumatic]] or [[hydraulic]]. An analog signal uses some property of the medium to convey the signal's information. For example, an [[aneroid barometer]] uses rotary position as the signal to convey pressure information.  In an electrical signal, the [[voltage]], [[Electric current|current]], or [[frequency]] of the signal may be varied to represent the information.
   
Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as [[sound]], [[light]], [[temperature]], position, or [[pressure]].  The physical variable is converted to an analog signal by a [[transducer]].   For example, in sound recording, fluctuations in air pressure (that is to say, [[sound]]) strike the diaphragm of a [[microphone]] which induces corresponding electrical fluctuations.  The voltage or the current is said to be an ''analog'' of the sound.

====Digital signal====
{{main|Digital signal}}
[[File:Original message.jpg|thumb|A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels]]
A digital signal is a signal that is constructed from a discrete set of [[waveform]]s of a physical quantity so as to represent a sequence of [[discrete space|discrete]] values.<ref>{{cite book |url=https://books.google.com/books?id=1eO7kLWUmYIC&q=digital%20signal%20logic&pg=PA4 |title=Digital Design with CPLD Applications and VHDL |author=Robert K. Dueck |archive-url=https://web.archive.org/web/20171217234501/https://books.google.com/books?id=1eO7kLWUmYIC&lpg=PA49&ots=EBhxEwk7bY&dq=digital%20signal%20logic&pg=PA4 |archive-date=2017-12-17 |quote=A digital representation can have only specific discrete values|isbn=1401840302 |year=2005 |publisher=Thomson/Delmar Learning }}</ref><ref>{{Cite book |title = Digital Signal Processing |url=https://books.google.com/books?id=H_5SAAAAMAAJ |publisher=Pearson Prentice Hall |date=2007-01-01 |isbn=9780131873742 |first1=John G. |last1=Proakis |first2=Dimitris G. |last2=Manolakis|author2-link= Dimitris Manolakis |url-status=live |archive-url=https://web.archive.org/web/20160520061336/https://books.google.com/books?id=H_5SAAAAMAAJ |archive-date=2016-05-20 |df=ymd}}</ref><ref name=waveform>{{cite book |url=https://books.google.com/books?id=WJ9qkNpScFAC&q=%22a+digital+signal+is%22+communication&pg=PA3  |title=Analogue and Digital Communication Techniques |archive-url=https://web.archive.org/web/20171217234501/https://books.google.com/books?id=WJ9qkNpScFAC&pg=PA3&dq=%22a+digital+signal+is%22+communication&hl=sv&sa=X&ved=0CFoQ6AEwB2oVChMI-MD09ZjjxwIVBAssCh1wnQu4 |archive-date=2017-12-17 |quote=A digital signal is a complex waveform and can be defined as a discrete waveform having a finite set of levels|isbn=9780080527147 |last1=Smillie |first1=Grahame |date=1999-04-02 |publisher=Elsevier }}</ref> A ''logic signal'' is a digital signal with only two possible values,<ref>{{cite web |url=http://www.chegg.com/homework-help/definitions/digital-signal-4 |title=Digital Signal |access-date=2016-08-13 |archive-date=2019-04-02 |archive-url=https://web.archive.org/web/20190402155546/https://www.chegg.com/homework-help/definitions/digital-signal-4 |url-status=live }}</ref><ref>{{cite book |title=The Art of Electronics |author1=Paul Horowitz |author2=Winfield Hill |isbn=9780521809269 |publisher=Cambridge University Press |date=2015}}</ref> and describes an arbitrary [[bit stream]]. Other types of digital signals can represent [[three-valued logic]] or higher valued logics.

Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity.<ref name=Khanna>{{cite book |author=Vinod Kumar Khanna |url=https://books.google.com/books?id=Vf2qXAbn58oC |title=Digital Signal Processing |date=2009 |isbn=9788121930956 |page=3 | publisher=S. Chand |quote=A digital signal is a special form of discrete-time signal which is discrete in both time and amplitude, obtained by permitting each value (sample) of a discrete-time signal to acquire a finite set of values (quantization), assigning it a numerical symbol according to a code ... A digital signal is a sequence or list of numbers drawn from a finite set.}}</ref> The physical quantity may be a variable electric current or voltage, the intensity, phase or [[polarization (waves)|polarization]] of an [[optical]] or other [[electromagnetism|electromagnetic field]], acoustic pressure, the [[magnetization]] of a [[magnetic storage]] media, etc. Digital signals are present in all [[digital electronics]], notably computing equipment and [[data transmission]].

With digital signals, system noise, provided it is not too great, will not affect system operation whereas noise always degrades the operation of [[analog signals]] to some degree.

Digital signals often arise via [[Sampling (signal processing)|sampling]] of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by an [[analog-to-digital converter]] circuit, wherein the circuit will read the voltage level on the line, say, every 50&nbsp;[[microseconds]] and represent each reading with a fixed number of bits. The resulting stream of numbers is stored as digital data on a discrete-time and quantized-amplitude signal.  [[Computer]]s and other [[Digital data|digital]] devices are restricted to discrete time.

=== Energy and power ===
According to the strengths of signals, practical signals can be classified into two categories: energy signals and power signals.<ref>{{Cite book|title=Digital communications : fundamentals and applications|last=Sklar |first= Bernard |date=2001|publisher=Prentice-Hall PTR|isbn=0130847887|edition= 2nd|location=Upper Saddle River, N.J.|oclc=45823120}}</ref>

Energy signals: Those signals' [[energy]] are equal to a finite positive value, but their average powers are 0;

<math>0 < E = \int_{-\infty }^{\infty } s^2(t)dt < \infty </math>

Power signals: Those signals' average [[Power (physics)|power]] are equal to a finite [[Sign (mathematics)|positive]] value, but their energy are [[Infinity|infinite]].

<math>P = \lim_{T\rightarrow  \infty} \frac{1}{T} \int_{-T/2 }^{T/2} s^2(t)dt </math>

=== Deterministic and random ===
Deterministic signals are those whose values at any time are predictable and can be calculated by a mathematical equation.

Random signals are signals that take on random values at any given time instant and must be modeled [[stochastic]]ally.<ref>{{Cite book|title=Principles of communication : systems, modulation, and noise|last=Ziemer |first=Rodger E.|last2=Tranter |first2=William H. |publisher=Wiley |isbn=9781118078914|edition= Seventh|location=Hoboken, New Jersey|oclc=856647730|date = 2014-03-17}}</ref>

=== Even and odd ===
{{multiple image
 | header            = Even and odd signals
 | image1            = Function x^2.svg
 | caption1          = <math>f(x)=x^2</math> is an example of an even signal.
 | image2            = Function-x3.svg
 | caption2          = <math>f(x)=x^3</math> is an example of an odd signal.
}}

An [[Even and odd functions|even signal]] satisfies the condition <math>x(t) = x(-t)</math>

or equivalently if the following equation holds for all <math>t</math> and <math>-t</math> in the domain of <math>x</math>:
:<math>x(t) - x(-t) = 0.</math>

An odd signal satisfies the condition <math>x(t) = - x(-t)</math>

or equivalently if the following equation holds for all <math>t</math> and <math>-t</math> in the domain of <math>x</math>:
:<math>x(t) + x(-t) = 0.</math>

=== Periodic ===
A signal is said to be [[Periodic function|periodic]] if it satisfies the condition:

<math>x(t) = x(t + T)\quad \forall t \in [t_0 , t_{max}]</math> or <math>x(n) = x(n + N)\quad \forall n \in [n_0 , n_{max}]</math>

Where:

<math>T</math> = fundamental time [[Period (physics)|period]],

<math>1/T = f </math>= fundamental [[frequency]].

The same can be applied to <math>N</math>. A periodic signal will repeat for every period.

==== Time discretization{{anchor|Discretization}} ====
[[File:Sampled.signal.svg|right|thumb|Discrete-time signal created from a continuous signal by [[Sampling (signal processing)|sampling]]]]

Signals can be classified as [[Continuous signal|continuous]] or [[discrete time]].  In the mathematical abstraction, the domain of a continuous-time signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (DT) signal is the set of [[integer]]s (or other subsets of real numbers).  What these integers represent depends on the nature of the signal; most often it is time.

A continuous-time signal is any [[mathematical function|function]] which is defined at every time ''t'' in an interval, most commonly an infinite interval. A simple source for a discrete-time signal is the [[Sampling (signal processing)|sampling]] of a continuous signal, approximating the signal by a sequence of its values at particular time instants.

=== Amplitude quantization{{anchor|Quantization}} ===
If a signal is to be represented as a sequence of digital data, it is impossible to maintain exact precision – each number in the sequence must have a finite number of digits.  As a result, the values of such a signal must be [[Quantization (signal processing)|quantized]] into a [[finite set]] for practical representation. Quantization is the process of converting a continuous analog audio signal to a digital signal with discrete numerical values of integers.

== Examples of signals ==
Naturally occurring signals can be converted to electronic signals by various [[sensor]]s. Examples include:
* ''[[Motion]]''.  The motion of an object can be considered to be a signal and can be monitored by various sensors to provide electrical signals.<ref name= Lu/> For example, [[radar]] can provide an electromagnetic signal for following aircraft motion.  A motion signal is one-dimensional (time), and the range is generally three-dimensional.  Position is thus a 3-vector signal; position and orientation of a rigid body is a 6-vector signal. Orientation signals can be generated using a [[gyroscope]].<ref name= gyro/>
* ''[[Sound]]''.  Since a sound is a [[oscillation|vibration]] of a medium (such as air), a sound signal associates a [[pressure]] value to every value of time and possibly three space coordinates indicating the direction of travel. A sound signal is converted to an electrical signal by a [[microphone]], generating a [[voltage]] signal as an analog of the sound signal. Sound signals can be [[sampling (signal processing)|sampled]] at a discrete set of time points; for example, [[compact disc]]s (CDs) contain discrete signals representing sound, recorded at [[44,100 Hz]]; since CDs are recorded in [[stereo]], each sample contains data for a left and right channel, which may be considered to be a 2-vector signal. The CD encoding is converted to an electrical signal by reading the information with a [[laser]], converting the sound signal to an optical signal.<ref name=Chambers/>
* ''[[Image]]s''.  A picture or image consists of a brightness or color signal, a function of a two-dimensional location. The object's appearance is presented as emitted or reflected [[light]], an electromagnetic signal. It can be converted to voltage or current waveforms using devices such as the [[charge-coupled device]].  A 2D image can have a continuous spatial domain, as in a traditional photograph or painting; or the image can be discretized in space, as in a [[digital image]].  Color images are typically represented as a combination of monochrome images in three [[primary colors]].
* ''[[Video]]s''. A video signal is a sequence of images. A point in a video is identified by its two-dimensional position in the image and by the time at which it occurs, so a video signal has a three-dimensional domain. Analog video has one continuous domain dimension (across a [[scan line]]) and two discrete dimensions (frame and line).
* Biological ''[[membrane potential]]s''.  The value of the signal is an [[electric potential]] (voltage).  The domain is more difficult to establish.  Some [[cell (biology)|cell]]s or [[organelle]]s have the same membrane potential throughout; [[neuron]]s generally have different potentials at different points.  These signals have very low energies, but are enough to make nervous systems work; they can be measured in aggregate by [[electrophysiology]] techniques.
*The output of a [[thermocouple]], which conveys temperature information.<ref name=Priemer/>
*The output of a [[pH meter]] which conveys acidity information.<ref name=Priemer/>

==Signal processing==
[[File:Signal processing system.png|thumb|400px|Signal transmission using electronic signals]]
{{main|Signal processing}}

Signal processing is the manipulation of signals. A common example is signal transmission between different locations. The embodiment of a signal in electrical form is made by a [[transducer]] that converts the signal from its original form to a [[waveform]] expressed as a [[Electric current|current]] or a [[voltage]], or [[electromagnetic radiation]], for example, an [[Free-space optical communication|optical signal]] or [[radio transmission]]. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as [[electronic amplifier]]s and [[electronic filters|filters]], and can be transmitted to a remote location by a [[transmitter]] and received using [[radio receiver]]s.

==Signals and systems==
In [[electrical engineering]] (EE) programs, signals are covered in a class and field of study known as ''signals and systems''. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous [[linear algebra]] and [[differential equation]] classes they have taken.<ref name="McMahon s and s">{{cite book|isbn=978-0-07-147578-5|url=https://www.amazon.com/gp/product/0071475788?selectObb=new|title=Signals & Systems Demystified|author=David McMahon|location=New York|publisher=McGraw Hill|year=2007|access-date=2017-09-11|archive-date=2020-01-22|archive-url=https://web.archive.org/web/20200122152613/https://www.amazon.com/gp/product/0071475788?selectObb=new|url-status=live}}</ref>

The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, frequency, ''s'' and ''z''. Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous-time signals (''t''), one might transform from the time domain to a frequency or ''s'' domain; or from discrete time (''n'') to frequency or ''z'' domains. Systems also can be transformed between these domains like signals, with continuous to ''s'' and discrete to ''z''.

Signals and systems is a subset of the field of [[mathematical model]]ing. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with [[dynamical system]]s tools including differential equations, and recently, [[Lagrangian mechanics|Lagrangians]]. Students are expected to understand the modeling tools as well as the mathematics, physics, circuit analysis, and transformations between the 8 domains.

Because mechanical engineering (ME) topics like friction, dampening etc. have very close analogies in signal science (inductance, resistance, voltage, etc.), many of the tools originally used in ME transformations (Laplace and Fourier transforms, Lagrangians, sampling theory, probability, difference equations, etc.) have now been applied to signals, circuits, systems and their components, analysis and design in EE. Dynamical systems that involve noise, filtering and other random or chaotic attractors and repellers have now placed stochastic sciences and statistics between the more deterministic discrete and continuous functions in the field. (Deterministic as used here means signals that are completely determined as functions of time).

EE taxonomists are still not decided where signals and systems falls within the whole field of signal processing vs. circuit analysis and mathematical modeling, but the common link of the topics that are covered in the course of study has brightened boundaries with dozens of books, journals, etc. called "Signals and Systems", and used as text and test prep for the EE, as well as, recently, computer engineering exams.<ref name="Signals and systems">{{cite book |isbn= 978-0073380681 |title= Signals and Systems: Analysis Using Transform Methods & MATLAB|author= M.J. Roberts |location=New York|publisher=McGraw Hill|year=2011}}</ref>

==Gallery==
<gallery widths="150px" heights="150px" perrow="4">
Signalman sends semaphore message from Pearl Harbor Control Tower c1960.jpg|A signalman sends a semaphore message from a Pearl Harbor Control Tower, {{circa|1960}}.
Finnish distant signal displaying Expect Stop.jpg|A Finnish distant signal at the western approach to [[Muhos]] station is displaying ''Expect Stop''.
Hailing a cab.jpg|A woman hailing a cab is sending a signal of availability to be picked up.
Signal flare during a rescue training mission.jpg|A [[flare]] is a common means to signal during dark or smoke-filled conditions.
</gallery>

==See also==
{{wikibooks|Signals and Systems}}
*{{anl|A Mathematical Theory of Communication}}
*[[Current loop]] – a signaling system in widespread use for process control
*[[Signal-to-noise ratio]]

== Notes ==
{{notelist}}

== References ==

{{Reflist | refs =

<ref name=Chambers>
The optical reading process is described by {{cite book |title=CD & DVD Recording for Dummies |url=https://books.google.com/books?id=VKsAroUnIxsC&pg=PA13 |page=13 |author=Mark L. Chambers |isbn=978-0764559563 |publisher=John Wiley & Sons |year=2004 |edition= 2nd |url-status=live |archive-url=https://web.archive.org/web/20130602154240/http://books.google.com/books?id=VKsAroUnIxsC&pg=PA13 |archive-date=2013-06-02 }}
</ref>

<ref name=PC>
{{cite journal |last1=Chakravorty |first1=Pragnan |title=What Is a Signal? [Lecture Notes] |journal=IEEE Signal Processing Magazine |year=2018 |volume=35 |issue=5 |pages=175–177 |doi=10.1109/MSP.2018.2832195 |bibcode=2018ISPM...35e.175C |s2cid=52164353 |quote=Consequently, a signal, represented as a function of one or more variables, may be defined as an observable change in a quantifiable entity.}}
</ref>

<ref name=gyro>
For example, see {{cite book |title=Advances in Gyroscope Technologies |author1=M. N. Armenise |author2=Caterina Ciminelli |author3=Francesco Dell'Olio |author4=Vittorio Passaro |chapter=§4.3 Optical gyros based on a fiber ring laser |chapter-url=https://books.google.com/books?id=lJUiyigJRBgC&pg=PA47 |page=47 |isbn=978-3642154935 |year=2010 |publisher=Springer |url-status=live |archive-url=https://web.archive.org/web/20130602165007/http://books.google.com/books?id=lJUiyigJRBgC&pg=PA47 |archive-date=2013-06-02 }}
</ref>

<ref name=IEEE>
{{cite journal |title=Aims and scope |journal=IEEE Transactions on Signal Processing |url=https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78 |publisher=[[IEEE]] |url-status=live |archive-url=https://web.archive.org/web/20120417233106/http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78 |archive-date=2012-04-17 }}
</ref>

<ref name=Lu>
For an example from robotics, see 
{{cite book
 |title         = Neural Information Processing: 18th International Conference, Iconip 2011, Shanghai, China, November 13–17, 2011
 |chapter-url           = https://books.google.com/books?id=cU4skcyGRFUC&pg=PA506
 |pages         = 506 ''ff''
 |chapter       = Analog–digital circuit for motion detection based on vertebrate retina and its application to mobile robot
 |author1       = K Nishio
 |author2       = T Yasuda
 |name-list-style = amp
 |editor1       = Bao-Liang Lu
 |editor2       = Liqing Zhang
 |editor3       = James Kwok
 |year          = 2011
 |publisher     = Springer
 |isbn          = 978-3642249648
 |url-status       = live
 |archive-url    = https://web.archive.org/web/20130602151534/http://books.google.com/books?id=cU4skcyGRFUC&pg=PA506
 |archive-date   = 2013-06-02
}}</ref>

<ref name=Sinha>{{cite book 
|title=Speech processing in embedded systems |url=https://books.google.com/books?id=mrOHsYChY-oC&pg=PA9 |page=9 |quote=To put it very generally, a signal is any time-varying physical quantity. |author=Priyabrata Sinha |isbn=978-0387755809 |year=2009 |publisher=Springer |url-status=live |archive-url=https://web.archive.org/web/20130602161013/http://books.google.com/books?id=mrOHsYChY-oC&pg=PA9 |archive-date=2013-06-02 }}
</ref>

<ref name=Priemer>
{{cite book |title=Introductory Signal Processing |author=Roland Priemer |url=https://books.google.com/books?id=QBT7nP7zTLgC&pg=PA1 |page=1 |isbn=978-9971509194 |year=1991 |publisher=World Scientific |url-status=live |archive-url=https://web.archive.org/web/20130602161539/http://books.google.com/books?id=QBT7nP7zTLgC&pg=PA1 |archive-date=2013-06-02 |quote=A signal is a function that conveys information about the behavior of a system or attributes of some phenomenon. }}
</ref>

<ref name=Wilmshurst>
{{cite book |title=Signal Recovery from Noise in Electronic Instrumentation |author=T. H. Wilmshurst |url=https://books.google.com/books?id=49hfsIPpGwYC&pg=PP11 |pages=11 ''ff'' |isbn=978-0750300582 |edition= 2nd |publisher=CRC Press |year=1990 |url-status=live |archive-url=https://web.archive.org/web/20150319012552/http://books.google.com/books?id=49hfsIPpGwYC&pg=PP11 |archive-date=2015-03-19 }}
</ref>

}}

==Further reading==

* {{cite book |author=Hsu, P. H. |title=Schaum's Theory and Problems: Signals and Systems |publisher=McGraw-Hill |date=1995 |isbn=0-07-030641-9}}
* {{cite book |author=Lathi, B.P. |title=Signal Processing & Linear Systems |publisher=Berkeley-Cambridge Press |date=1998 |isbn=0-941413-35-7}}

{{Authority control}}

[[Category:Engineering concepts]]
[[Category:Digital signal processing]]
[[Category:Signal processing]]
[[Category:Telecommunication theory]]