Editing Signal (section)

== 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.