Signal

Last updated January 28, 2024

Signal refers to both the process and the result of transmission of data over some 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.^[1] Any quantity that can vary over space or time can be used as a signal to share messages between observers.^[2] The IEEE Transactions on Signal Processing includes audio, video, speech, image, sonar, and radar as examples of signals.^[3] A signal may also be defined as any observable change in a quantity over space or time (a time series), even if it does not carry information.^{[lower-alpha 1]}

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 speaker does the reverse.^[1]

Another important property of a signal is its 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, 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,^[5] 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 transmission, 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 design engineering developed to address the functional design of signals in user–machine interfaces.

Definitions

Definitions specific to sub-fields are common:

In electronics and telecommunications, signal refers to any time-varying voltage, 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 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, 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^{[ 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 as time series 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, a 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).^[2]

In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into analog signals and digital signals; 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

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. Digital-signal-noise.svg — 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 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 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, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values.^[6]^[7]

The term analog signal usually refers to electrical signals; however, analog signals may use other mediums such as 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, 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

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 waveforms of a physical quantity so as to represent a sequence of discrete values.^[8]^[9]^[10] A logic signal is a digital signal with only two possible values,^[11]^[12] 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.^[13] The physical quantity may be a variable electric current or voltage, the intensity, phase or polarization of an optical or other 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 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 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 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.^[14]

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

$0<E=\int _{-\infty }^{\infty }s^{2}(t)dt<\infty$

Power signals: Those signals' average power are equal to a finite positive value, but their energy are infinite.

$P=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{-T/2}^{T/2}s^{2}(t)dt$

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 stochastically.^[15]

Even and odd

Even and odd signals

f(x)=x^{2}

is an example of an even signal.

f(x)=x^{3}

is an example of an odd signal.

An even signal satisfies the condition $x(t)=x(-t)$

or equivalently if the following equation holds for all $t$ and $-t$ in the domain of $x$ :

x(t)-x(-t)=0.

An odd signal satisfies the condition $x(t)=-x(-t)$

or equivalently if the following equation holds for all $t$ and $-t$ in the domain of $x$ :

x(t)+x(-t)=0.

Periodic

A signal is said to be periodic if it satisfies the condition:

$x(t)=x(t+T)$ or $x(n)=x(n+N)$

Where:

$T$ = fundamental time period,

$1/T=f$ = fundamental frequency.

A periodic signal will repeat for every period.

Time discretization

Discrete-time signal created from a continuous signal by sampling Sampled.signal.svg — Discrete-time signal created from a continuous signal by sampling

Signals can be classified as 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 integers (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 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 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 sensors. 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 a gyroscope.^[17]
Sound . Since a sound is a 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 sampled at a discrete set of time points; for example, compact discs (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.^[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 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.
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 a scan line) and two discrete dimensions (frame and line).
Biological membrane potentials . The value of the signal is an electric potential (voltage). The domain is more difficult to establish. Some cells or organelles 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 by electrophysiology techniques.
The output of a thermocouple, which conveys temperature information.^[1]
The output of a pH meter which conveys acidity information.^[1]

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 current or a voltage, or electromagnetic radiation, for example, an optical signal or radio transmission. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as electronic amplifiers and filters, and can be transmitted to a remote location by a transmitter and received using radio receivers.

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.^[19]

The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, requency, 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 modeling. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with dynamical 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]

Gallery

A signalman sends a semaphore message from a Pearl Harbor Control Tower, c. 1960.
A Finnish distant signal at the western approach to Muhos station is displaying Expect Stop.
A woman hailing a cab is sending a signal of availability to be picked up.
A flare is a common means to signal during dark or smoke-filled conditions.

Notes

↑ Some authors do not emphasize the role of information in the definition of a signal.^[4]

Related Research Articles

An analog signal is any continuous-time signal representing some other quantity, i.e., analogous to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies continuously with the pressure of the sound waves.

<span class="mw-page-title-main">Digital data</span> Discrete, discontinuous representation of information

Digital data, in information theory and information systems, is information represented as a string of discrete symbols, each of which can take on one of only a finite number of values from some alphabet, such as letters or digits. An example is a text document, which consists of a string of alphanumeric characters. The most common form of digital data in modern information systems is binary data, which is represented by a string of binary digits (bits) each of which can have one of two values, either 0 or 1.

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant in which case they can be analyzed exactly using LTI system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies, they are sometimes known as frequency filters.

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a separate signal called the modulation signal that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer.

Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality, and to also detect or pinpoint components of interest in a measured signal.

In electronics, an analog-to-digital converter 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 an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals.

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band.

Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is a method of controlling the average power or amplitude delivered by an electrical signal. The average value of voltage fed to the load is controlled by switching the supply between 0 and 100% at a rate faster than it takes the load to change significantly. The longer the switch is on, the higher the total power supplied to the load. Along with maximum power point tracking (MPPT), it is one of the primary methods of controlling the output of solar panels to that which can be utilized by a battery. PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching. The goal of PWM is to control a load; however, the PWM switching frequency must be selected carefully in order to smoothly do so.

<span class="mw-page-title-main">Digital-to-analog converter</span> Device that converts a digital signal into an analog signal

In electronics, a digital-to-analog converter is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values.

Analog signal processing is a type of signal processing conducted on continuous analog signals by some analog means. "Analog" indicates something that is mathematically represented as a set of continuous values. This differs from "digital" which uses a series of discrete quantities to represent signal. Analog values are typically represented as a voltage, electric current, or electric charge around components in the electronic devices. An error or noise affecting such physical quantities will result in a corresponding error in the signals represented by such physical quantities.

Analogue electronics are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term analogue describes the proportional relationship between a signal and a voltage or current that represents the signal. The word analogue is derived from the Greek word ανάλογος analogos meaning proportional.

Delta-sigma modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency as part of the process of delta-sigma analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Delta-sigma modulation achieves high quality by utilizing a negative feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies well above the original signal's bandwidth. Subsequent low-pass filtering for demodulation easily removes this high frequency noise and time averages to achieve high accuracy in amplitude which can be ultimately encoded as pulse-code modulation (PCM).

In signal processing, a nonlinearfilter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs.

The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication.

Analog devices are a combination of both analog machine and analog media that can together measure, record, reproduce, receive or broadcast continuous information, for example, the almost infinite number of grades of transparency, voltage, resistance, rotation, or pressure. In theory, the continuous information in an analog signal has an infinite number of possible values with the only limitation on resolution being the accuracy of the analog device.

<span class="mw-page-title-main">Digital signal</span> Signal used to represent data as a sequence of discrete values

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 any given time it represents a real number within a continuous range of values.

In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.

This glossary of electrical and electronics engineering is a list of definitions of terms and concepts related specifically to electrical engineering and electronics engineering. For terms related to engineering in general, see Glossary of engineering.

References

1 2 3 4 Roland Priemer (1991). Introductory Signal Processing. World Scientific. p. 1. ISBN 978-9971509194. 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.
1 2 Chakravorty, 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. S2CID 52164353. Consequently, a signal, represented as a function of one or more variables, may be defined as an observable change in a quantifiable entity.
↑ "Aims and scope". IEEE Transactions on Signal Processing. IEEE. Archived from the original on 2012-04-17.
↑ Priyabrata Sinha (2009). Speech processing in embedded systems. Springer. p. 9. ISBN 978-0387755809. Archived from the original on 2013-06-02. To put it very generally, a signal is any time-varying physical quantity.
↑ T. H. Wilmshurst (1990). Signal Recovery from Noise in Electronic Instrumentation (2nd ed.). CRC Press. pp. 11 ff. ISBN 978-0750300582. Archived from the original on 2015-03-19.
↑ "Digital signals". www.st-andrews.ac.uk. Archived from the original on 2017-03-02. Retrieved 2017-12-17.
↑ "Analog vs. Digital - learn.sparkfun.com". learn.sparkfun.com. Archived from the original on 2017-07-05. Retrieved 2017-12-17.
↑ Robert K. Dueck (2005). Digital Design with CPLD Applications and VHDL. Thomson/Delmar Learning. ISBN 1401840302. Archived from the original on 2017-12-17. A digital representation can have only specific discrete values
↑ Proakis, John G.; Manolakis, Dimitris G. (2007-01-01). Digital Signal Processing. Pearson Prentice Hall. ISBN 9780131873742. Archived from the original on 2016-05-20.
↑ Smillie, Grahame (1999-04-02). Analogue and Digital Communication Techniques. Elsevier. ISBN 9780080527147. Archived from the original on 2017-12-17. A digital signal is a complex waveform and can be defined as a discrete waveform having a finite set of levels
↑ "Digital Signal". Archived from the original on 2019-04-02. Retrieved 2016-08-13.
↑ Paul Horowitz; Winfield Hill (2015). The Art of Electronics. Cambridge University Press. ISBN 9780521809269.
↑ Vinod Kumar Khanna (2009). Digital Signal Processing. S. Chand. p. 3. ISBN 9788121930956. 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, 1927– (2001). Digital communications : fundamentals and applications (2nd ed.). Upper Saddle River, N.J.: Prentice-Hall PTR. ISBN 0130847887. OCLC 45823120.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
↑ Ziemer, Rodger E. (2014-03-17). Principles of communication : systems, modulation, and noise. Tranter, William H. (Seventh ed.). Hoboken, New Jersey. ISBN 9781118078914. OCLC 856647730.{{cite book}}: CS1 maint: location missing publisher (link)
↑ For an example from robotics, see K Nishio & T Yasuda (2011). "Analog–digital circuit for motion detection based on vertebrate retina and its application to mobile robot". In Bao-Liang Lu; Liqing Zhang & James Kwok (eds.). Neural Information Processing: 18th International Conference, Iconip 2011, Shanghai, China, November 13–17, 2011. Springer. pp. 506 ff. ISBN 978-3642249648. Archived from the original on 2013-06-02.
↑ For example, see M. N. Armenise; Caterina Ciminelli; Francesco Dell'Olio; Vittorio Passaro (2010). "§4.3 Optical gyros based on a fiber ring laser". Advances in Gyroscope Technologies. Springer. p. 47. ISBN 978-3642154935. Archived from the original on 2013-06-02.
↑ The optical reading process is described by Mark L. Chambers (2004). CD & DVD Recording for Dummies (2nd ed.). John Wiley & Sons. p. 13. ISBN 978-0764559563. Archived from the original on 2013-06-02.
↑ David McMahon (2007). Signals & Systems Demystified. New York: McGraw Hill. ISBN 978-0-07-147578-5. Archived from the original on 2020-01-22. Retrieved 2017-09-11.
↑ M.J. Roberts (2011). Signals and Systems: Analysis Using Transform Methods & MATLAB. New York: McGraw Hill. ISBN 978-0073380681.