![William Powell Frith The signal 1858](https://upload.wikimedia.org/wikipedia/commons/8/83/William_Powell_Frith_The_signal_1858.jpg)
In
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...
, a signal is a function that conveys
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
about a phenomenon.
[ Any quantity that can vary over space or time can be used as a signal to share messages between observers.][ The '']IEEE Transactions on Signal Processing
The ''IEEE Transactions on Signal Processing'' is a biweekly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers covering research on signal processing. It was established in 1953 as the ''IRE Transac ...
'' includes audio
Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to:
Sound
*Audio signal, an electrical representation of sound
*Audio frequency, a frequency in the audio spectrum
*Digital audio, representation of sound ...
, video
Video is an electronic medium for the recording, copying, playback, broadcasting, and display of moving visual media. Video was first developed for mechanical television systems, which were quickly replaced by cathode-ray tube (CRT) syste ...
, speech, image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
, sonar
Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigation, navigate, measure distances (ranging), communicate with or detect o ...
, and radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
as examples of signal. A signal may also be defined as observable change in a quantity over space or time (a time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
), even if it does not carry information.
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
In biology, cell signaling (cell signalling in British English) or cell communication is the ability of a cell to receive, process, and transmit signals with its environment and with itself. Cell signaling is a fundamental property of all cellula ...
. Signaling theory
Within evolutionary biology, signalling theory is a body of theoretical work examining communication between individuals, both within species and across species. The central question is when organisms with conflicting interests, such as in sex ...
, in evolutionary biology
Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life fo ...
, proposes that a substantial driver for evolution
Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
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
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
, and often the original form of a signal is converted to another form of energy using a transducer
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and contr ...
. For example, a microphone
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
converts an acoustic signal to a voltage waveform, and a speaker
Speaker may refer to:
Society and politics
* Speaker (politics), the presiding officer in a legislative assembly
* Public speaker, one who gives a speech or lecture
* A person producing speech: the producer of a given utterance, especially:
** I ...
does the reverse.
Another important property of a signal is its entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
or information content
In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. It can be thought of as an alternative wa ...
. Information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
serves as the formal study of signals and their content. The information of a signal is often accompanied by noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (crosstalk
In electronics, crosstalk is any phenomenon by which a signal transmitted on one circuit or channel of a transmission system creates an undesired effect in another circuit or channel. Crosstalk is usually caused by undesired capacitive, induc ...
). The reduction of noise is covered in part under the heading of signal integrity
Signal integrity or SI is a set of measures of the quality of an electrical signal. In digital electronics, a stream of binary values is represented by a voltage (or current) waveform. However, digital signals are fundamentally analog in nature, ...
. The separation of desired signals from background noise is the field of signal recovery, one branch of which is estimation theory
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their valu ...
, a probabilistic approach to suppressing random disturbances.
Engineering disciplines such as electrical engineering have advanced the design, study, and implementation of systems involving transmission
Transmission may refer to:
Medicine, science and technology
* Power transmission
** Electric power transmission
** Propulsion transmission, technology allowing controlled application of power
*** Automatic transmission
*** Manual transmission
*** ...
, storage, and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines: electronic engineering
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...
and computer engineering
Computer engineering (CoE or CpE) is a branch of electrical engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers ...
developed to specialize in the design and analysis of systems that manipulate physical signals, while design engineering
A design engineer is an engineer focused on the engineering design process in any of the various engineering disciplines (including civil, mechanical, electrical, chemical, textiles, aerospace, nuclear, manufacturing, systems, and structural /buil ...
developed to address the functional design of signals in user–machine interfaces.
Definitions
Definitions specific to sub-fields are common:
* In electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
and telecommunications
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
, ''signal'' refers to any time-varying voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
, current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
, or electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
that carries information.
* In signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...
, signals are analog and digital representations of analog physical quantities.
* In information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
, a signal is a codified message, that is, the sequence of states in a communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
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
"Mary Had a Little Lamb" is an English language nursery rhyme of nineteenth-century American origin, first published by American writer Sarah Josepha Hale in 1830. It has a Roud Folk Song Index number of 7622.
Background
The nursery rhyme was ...
" might be the message spoken into a telephone
A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into e ...
. 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
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
, for example common-channel signaling
In telecommunication, common-channel signaling (CCS), or common-channel interoffice signaling (CCIS), is the transmission of control information ''( signaling)'' via a separate channel than that used for the messages, The signaling channel usually ...
, 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 distinction is between discrete and continuous spaces that the functions are defined over, for example, discrete and continuous-time domains. Discrete-time signals are often referred to as ''time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
'' in other fields. Continuous-time signals are often referred to as ''continuous signals''.
A second important distinction is between discrete-valued and continuous-valued. Particularly in digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...
, a digital signal
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at ...
may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In digital electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals.
Digital electronic circuits are usual ...
, 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).[
In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into ]analog signal
An analog signal or analogue signal (see spelling differences) is any continuous signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies c ...
s and digital signal
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at ...
s; according to the determinacy of signals, classified into deterministic signals and random signals; according to the strength of signals, classified into energy signals and power signals.
Analog and digital signals
Two main types of signals encountered in practice are ''analog
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use analog ...
'' and '' digital''. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals are '' quantized'', while analog signals are continuous.
Analog signal
An analog signal is any continuous signal
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
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
An audio signal is a representation of sound, typically using either a changing level of electrical voltage for analog signals, or a series of binary numbers for digital signals. Audio signals have frequencies in the audio frequency range of r ...
, the instantaneous voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
of the signal varies continuously with the sound pressure
Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone ...
. It differs from a digital signal
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at ...
, in which the continuous quantity is a representation of a sequence of discrete value
In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by ''measuring'' or ''counting'', respectively. If it can take on two particular real values such that it can also take on all ...
s which can only take on one of a finite number of values.
The term ''analog signal'' usually refers to electrical signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
s; however, analog signals may use other mediums such as mechanical
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations of ...
, pneumatic
Pneumatics (from Greek ‘wind, breath’) is a branch of engineering that makes use of gas or pressurized air.
Pneumatic systems used in Industrial sector, industry are commonly powered by compressed air or compressed inert gases. A central ...
or hydraulic
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...
. An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer
A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
, current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
, or frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
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
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
, light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
, position, or pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
. The physical variable is converted to an analog signal by a transducer
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and contr ...
. For example, in sound recording, fluctuations in air pressure (that is to say, sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
) strike the diaphragm of a microphone
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
which induces corresponding electrical fluctuations. The voltage or the current is said to be an ''analog'' of the sound.
Digital signal
A digital signal is a signal that is constructed from a discrete set of waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
s of a physical quantity so as to represent a sequence of discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
* Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
values. A ''logic signal'' is a digital signal with only two possible values, and describes an arbitrary bit stream
A bitstream (or bit stream), also known as binary sequence, is a sequence of bits.
A bytestream is a sequence of bytes. Typically, each byte is an 8-bit quantity, and so the term octet stream is sometimes used interchangeably. An octet may ...
. Other types of digital signals can represent three-valued logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate ...
or higher valued logics.
Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity. The physical quantity may be a variable electric current or voltage, the intensity, phase or polarization of an optical
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
or other electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
, acoustic pressure, the magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
of a magnetic storage
Magnetic storage or magnetic recording is the storage of data on a magnetized medium. Magnetic storage uses different patterns of magnetisation in a magnetizable material to store data and is a form of non-volatile memory. The information is acc ...
media, etc. Digital signals are present in all digital electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals.
Digital electronic circuits are usual ...
, notably computing equipment and data transmission
Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point o ...
.
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
An analog signal or analogue signal (see spelling differences) is any continuous signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies ...
to some degree.
Digital signals often arise via sampling of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by an analog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
circuit, wherein the circuit will read the voltage level on the line, say, every 50 microseconds
A microsecond is a unit of time in the International System of Units (SI) equal to one millionth (0.000001 or 10−6 or ) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available.
A microsecond is equal to 1000 n ...
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
A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...
s and other 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.
Energy signals: Those signals' energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
are equal to a finite positive value, but their average powers are 0;
Power signals: Those signals' average power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
are equal to a finite positive
Positive is a property of positivity and may refer to:
Mathematics and science
* Positive formula, a logical formula not containing negation
* Positive number, a number that is greater than 0
* Plus sign, the sign "+" used to indicate a posi ...
value, but their energy are infinite
Infinite may refer to:
Mathematics
* Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
.
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
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
ally.
Even and odd
An even signal satisfies the condition
or equivalently if the following equation holds for all and in the domain of :
:
An odd signal satisfies the condition
or equivalently if the following equation holds for all and in the domain of :
:
Periodic
A signal is said to be periodic if it satisfies the condition:
or
Where:
= fundamental time period
Period may refer to:
Common uses
* Era, a length or span of time
* Full stop (or period), a punctuation mark
Arts, entertainment, and media
* Period (music), a concept in musical composition
* Periodic sentence (or rhetorical period), a concept ...
,
= fundamental frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
.
A periodic signal will repeat for every period.
Time discretization
Signals can be classified as continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
or discrete time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
. 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
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
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 function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
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 of a continuous signal, approximating the signal by a sequence of its values at particular time instants.
Amplitude 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 quantized into a finite set
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,
:\
is a finite set with five elements. Th ...
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
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
s. Examples include:
* ''Motion
In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and mea ...
''. The motion of an object can be considered to be a signal and can be monitored by various sensors to provide electrical signals.[ For example, ]radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
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
A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rota ...
.[
* '']Sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
''. Since a sound is a vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...
of a medium (such as air), a sound signal associates a pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
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
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
, generating a voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
signal as an analog of the sound signal. Sound signals can be sampled
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of so ...
at a discrete set of time points; for example, compact disc
The compact disc (CD) is a Digital media, digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then rele ...
s (CDs) contain discrete signals representing sound, recorded at 44,100 Hz; since CDs are recorded in stereo
Stereophonic sound, or more commonly stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible perspective. This is usually achieved by using two independent audio channels through a configuration ...
, 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
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
, converting the sound signal to an optical signal.[
* '']Image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
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
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, an electromagnetic signal. It can be converted to voltage or current waveforms using devices such as the charge-coupled device
A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...
. 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
A digital image is an image composed of picture elements, also known as ''pixels'', each with ''finite'', '' discrete quantities'' of numeric representation for its intensity or gray level that is an output from its two-dimensional functions ...
. Color images are typically represented as a combination of monochrome images in three primary colors
A set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a br ...
.
* ''Video
Video is an electronic medium for the recording, copying, playback, broadcasting, and display of moving visual media. Video was first developed for mechanical television systems, which were quickly replaced by cathode-ray tube (CRT) syste ...
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
A scan line (also scanline) is one line, or row, in a raster scanning pattern, such as a line of video on a cathode ray tube (CRT) display of a television set or computer monitor.
On CRT screens the horizontal scan lines are visually discernible ...
) and two discrete dimensions (frame and line).
* Biological ''membrane potential
Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges ...
s''. The value of the signal is an electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
(voltage). The domain is more difficult to establish. Some cell
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery ...
s or organelle
In cell biology, an organelle is a specialized subunit, usually within a cell, that has a specific function. The name ''organelle'' comes from the idea that these structures are parts of cells, as organs are to the body, hence ''organelle,'' the ...
s have the same membrane potential throughout; neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
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 the techniques of electrophysiology
Electrophysiology (from Greek , ''ēlektron'', "amber" etymology of "electron"">Electron#Etymology">etymology of "electron" , ''physis'', "nature, origin"; and , '' -logia'') is the branch of physiology that studies the electrical properties of b ...
.
*The output of a thermocouple
A thermocouple, also known as a "thermoelectrical thermometer", is an electrical device consisting of two dissimilar electrical conductors forming an electrical junction. A thermocouple produces a temperature-dependent voltage as a result of the ...
, which conveys temperature information.[
*The output of a ]pH meter
A pH meter is a scientific instrument that measures the hydrogen-ion activity in water-based solutions, indicating its acidity or alkalinity expressed as pH. The pH meter measures the difference in electrical potential between a pH elect ...
which conveys acidity information.[
]
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
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and contr ...
that converts the signal from its original form to a waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
expressed as a current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
or a voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
, or electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, for example, an optical signal or radio transmission
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitt ...
. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as electronic amplifiers
Electronic may refer to:
*Electronics, the science of how to control electric energy in semiconductor
* ''Electronics'' (magazine), a defunct American trade journal
*Electronic storage, the storage of data using an electronic device
*Electronic co ...
and filters
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
, and can be transmitted to a remote location by a transmitter
In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna (radio), antenna. The transmitter itself generates a radio frequency alternating current, which i ...
and received using radio receivers
In radio communications, a radio receiver, also known as a receiver, a wireless, or simply a radio, is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. The ...
.
Signals and systems
In Electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
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
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices.
...
and differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
classes they have taken.
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
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
ing. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with Dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
s tools including differential equations, and recently, 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 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.
See also
*
*Current loop
In electrical signalling an analog current loop is used where a device must be monitored or controlled remotely over a pair of conductors. Only one current level can be present at any time.
A major application of current loops is the industry de ...
– a signaling system in widespread use for process control
*Signal-to-noise ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...
Notes
References
Further reading
*
*
{{Authority control
Engineering concepts
Digital signal processing
Signal processing
Telecommunication theory