In signal processing, a signal is a function that conveysinformation about a phenomenon.[1] Any quantity that can vary over space or time can be used as a signal to share messages between observers.[2] TheIEEE Transactions on Signal Processing includesaudio,video, speech,image,sonar, andradar as examples of signals.[3] A signal may also be defined asany observable change in a quantity over space or time (atime series), even if it does not carry information.[a]
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, withcell signaling.Signaling theory, inevolutionary biology, proposes that a substantial driver forevolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically provided by asensor, and often the original form of a signal is converted to another form of energy using atransducer. For example, amicrophone converts an acoustic signal to a voltage waveform, and aspeaker does the reverse.[1]
Another important property of a signal is itsentropy orinformation content.Information theory serves as the formal study of signals and their content. The information of a signal is often accompanied bynoise, 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 ofsignal integrity. The separation of desired signals from background noise is the field ofsignal recovery,[5] one branch of which isestimation theory, a probabilistic approach to suppressing random disturbances.
Engineering disciplines such as electrical engineering have advanced the design, study, and implementation of systems involvingtransmission,storage, and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines:electronic engineering andcomputer engineering developed to specialize in the design and analysis of systems that manipulate physical signals, whiledesign engineering developed to address the functional design of signals inuser–machine interfaces.
In a communication system, atransmitter encodes amessage to create a signal, which is carried to areceiver by the communication channel. For example, the words "Mary had a little lamb" might be the message spoken into atelephone. 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, for examplecommon-channel signaling, refers to phone number and other digital control information rather than the actual voice signal.
Signals can be categorized in various ways. The most common[verification needed] 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 astime series in other fields.Continuous-time signals are often referred to ascontinuous signals.
A second important distinction is between discrete-valued and continuous-valued. Particularly indigital signal processing, adigital signal may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. Indigital 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).[2]
In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified intoanalog signals anddigital signals; according to the determinacy of signals, classified into deterministic signals and random signals; according to thestrength of signals, classified into energy signals and power signals.
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 areanalog anddigital. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals arequantized, while analog signals are continuous.
An analog signal is anycontinuous 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 analogaudio signal, the instantaneousvoltage of the signal varies continuously with thesound pressure. It differs from adigital signal, in which the continuous quantity is a representation of a sequence ofdiscrete values which can only take on one of a finite number of values.[6][7]
The termanalog signal usually refers toelectrical signals; however, analog signals may use other mediums such asmechanical,pneumatic orhydraulic. An analog signal uses some property of the medium to convey the signal's information. For example, ananeroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, thevoltage,current, orfrequency 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 assound,light,temperature, position, orpressure. The physical variable is converted to an analog signal by atransducer. For example, in sound recording, fluctuations in air pressure (that is to say,sound) strike the diaphragm of amicrophone which induces corresponding electrical fluctuations. The voltage or the current is said to be ananalog of the sound.
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 ofwaveforms of a physical quantity so as to represent a sequence ofdiscrete values.[8][9][10] Alogic signal is a digital signal with only two possible values,[11][12] and describes an arbitrarybit stream. Other types of digital signals can representthree-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.[13] The physical quantity may be a variable electric current or voltage, the intensity, phase orpolarization of anoptical or otherelectromagnetic field, acoustic pressure, themagnetization of amagnetic storage media, etc. Digital signals are present in alldigital electronics, notably computing equipment anddata transmission.
With digital signals, system noise, provided it is not too great, will not affect system operation whereas noise always degrades the operation ofanalog signals to some degree.
Digital signals often arise viasampling of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by ananalog-to-digital converter circuit, wherein the circuit will read the voltage level on the line, say, every 50 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.Computers and otherdigital devices are restricted to discrete time.
Discrete-time signal created from a continuous signal bysampling
Signals can be classified ascontinuous ordiscrete 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 ofintegers (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 anyfunction which is defined at every timet in an interval, most commonly an infinite interval. A simple source for a discrete-time signal is thesampling of a continuous signal, approximating the signal by a sequence of its values at particular time instants.
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 bequantized into afinite 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.
Naturally occurring signals can be converted to electronic signals by varioussensors. 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.[16] 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 agyroscope.[17]
Sound. Since a sound is avibration of a medium (such as air), a sound signal associates apressure 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 amicrophone, generating avoltage signal as an analog of the sound signal. Sound signals can besampled at a discrete set of time points; for example,compact discs (CDs) contain discrete signals representing sound, recorded at44,100 Hz; since CDs are recorded instereo, 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 alaser, converting the sound signal to an optical signal.[18]
Images. 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 reflectedlight, an electromagnetic signal. It can be converted to voltage or current waveforms using devices such as thecharge-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 adigital image. Color images are typically represented as a combination of monochrome images in threeprimary colors.
Videos. 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 ascan line) and two discrete dimensions (frame and line).
Biologicalmembrane potentials. The value of the signal is anelectric potential (voltage). The domain is more difficult to establish. Somecells ororganelles have the same membrane potential throughout;neurons 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 byelectrophysiology techniques.
The output of athermocouple, which conveys temperature information.[1]
The output of apH meter which conveys acidity information.[1]
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 atransducer that converts the signal from its original form to awaveform expressed as acurrent or avoltage, orelectromagnetic radiation, for example, anoptical signal orradio transmission. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such aselectronic amplifiers andfilters, and can be transmitted to a remote location by atransmitter and received usingradio receivers.
Inelectrical engineering (EE) programs, signals are covered in a class and field of study known assignals 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 previouslinear algebra anddifferential equation classes they have taken.[19]
The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, frequency,s andz. 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 ors domain; or from discrete time (n) to frequency orz domains. Systems also can be transformed between these domains like signals, with continuous tos and discrete toz.
Signals and systems is a subset of the field ofmathematical modeling. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago withdynamical systems 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 (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.[20]
^abcdRoland Priemer (1991).Introductory Signal Processing. World Scientific. p. 1.ISBN978-9971509194.Archived from the original on 2013-06-02.A signal is a function that conveys information about the behavior of a system or attributes of some phenomenon.
^abChakravorty, Pragnan (2018). "What Is a Signal? [Lecture Notes]".IEEE Signal Processing Magazine.35 (5):175–177.Bibcode:2018ISPM...35e.175C.doi:10.1109/MSP.2018.2832195.S2CID52164353.Consequently, a signal, represented as a function of one or more variables, may be defined as an observable change in a quantifiable entity.
^Paul Horowitz; Winfield Hill (2015).The Art of Electronics. Cambridge University Press.ISBN9780521809269.
^Vinod Kumar Khanna (2009).Digital Signal Processing. S. Chand. p. 3.ISBN9788121930956.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.
^Sklar, Bernard (2001).Digital communications : fundamentals and applications (2nd ed.). Upper Saddle River, N.J.: Prentice-Hall PTR.ISBN0130847887.OCLC45823120.
^Ziemer, Rodger E.; Tranter, William H. (2014-03-17).Principles of communication : systems, modulation, and noise (Seventh ed.). Hoboken, New Jersey: Wiley.ISBN9781118078914.OCLC856647730.
