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Encyclopedia > Signal (electrical engineering)

In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying quantity. Signals are often scalar-valued functions of time (waveforms), but may be vector valued and may be functions of any other relevant independent variable. Telecommunication involves the transmission of signals over a distance for the purpose of communication. ... Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ... This article treats electronics engineering as a subfield of electrical engineering, though this is not typical use in some areas. ... Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ...

The concept is broad, and hard to define precisely. Definitions specific to subfields are common. For example, in information theory, a signal is a codified message, ie, the sequence of states in a communications channel that encodes a message. In a communications system, a transmitter encodes a message into a signal, which is carried to a receiver by the communications 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 voltage signal. The signal is transmitted to the receiving telephone by wires; and at the receiver it is reconverted into sounds. To meet Wikipedias quality standards, this article or section may require cleanup. ... Mary had a little lamb is a popular nursery rhyme. ... Josephson junction array chip developed by NIST as a standard volt. ...

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 other fields. Continuous-time signals are often referred to as continuous signals even when the signal functions are not continuous; an example is a square-wave signal. In statistics and signal processing, a time series is a sequence of data points, measured typically at successive times, spaced apart at uniform time intervals. ... In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ...

A second important distinction is between discrete-valued and continuous-valued. Digital signals are discrete-valued, but are often derived from an underlying continuous-valued physical process. A digital signal is a signal that is both discrete and quantized. ...

## Discrete-time and Continuous-time signals GA_googleFillSlot("encyclopedia_square");

If for a signal, the quantities are defined only on a discrete set of times, we call it a discrete-time signal. In other words, a discrete-time real (or complex) signal can be seen as a function from the set of integers to the set of real (or complex) numbers.

A continuous-time real (or complex) signal is any real-valued (or complex-valued) function which is defined for all time t in an interval, most commonly an infinite interval.

## Analog and digital signals

Less formally than the theoretical distinctions mentioned above, two main types of signals encountered in practice are analog and digital. In short, the difference between them is that digital signals are discrete and quantized, as defined below, while analog signals possess neither property. An analog or analogue signal is any continuously variable signal. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ...

### Discretization

Main article: Discrete signal

One of the fundamental distinctions between different types of signals is between continuous and discrete time. In the mathematical abstraction, the domain of a continuous-time (CT) signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time signal is the set of integers (or some interval). What these integers represent depends on the nature of the signal. A discrete signal is a signal that has been sampled from a continuous signal. ... Continuous time occurs when time is sampled continuously. ... Discrete time is non-continuous time. ... The integers consist of the positive natural numbers (1, 2, 3, â€¦), their negatives (âˆ’1, âˆ’2, âˆ’3, ...) and the number zero. ...

DT signals often arise via of CT signals. For instance, sensors output data continuously, but since a continuous stream may be difficult to record, a discrete-time signal is often used as an approximation. Computers and other digital devices are restricted to discrete time. To meet Wikipedias quality standards, this article or section may require cleanup. ... A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ... A digital system is one that uses discrete numbers, especially binary numbers, or non-numeric symbols such as letters or icons, for input, processing, transmission, storage, or display, rather than a continuous spectrum of values (an analog system). ...

### Quantization

If a signal is to be represented as a sequence of numbers, it is impossible to maintain arbitrarily high precision - each number in the sequence must have a finite number of digits. As a result, the values of such a signal are restricted to belong to a finite set; in other words, it is quantized. Quantization of x using Q(x) = floor(Lx)/L. In digital signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values; that is, converting an analog signal to a digital one via analog-to-digital conversion. ... In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... Quantization of x using Q(x) = floor(Lx)/L. In digital signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values; that is, converting an analog signal to a digital one via analog-to-digital conversion. ...

## Examples of signals

• Motion. The motion of a particle through some space can be considered to be a signal, or can be represented by a signal. The domain of a motion signal is one-dimensional (time), and the range is generally three-dimensional. Position is thus a 3-vector signal; position and orientation is a 6-vector signal.
• 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 three space coordinates. A microphone converts sound pressure at some place to just a function of time, using a voltage signal as an analog of the sound signal.
• Compact discs (CDs). CDs contain discrete signals representing sound, recorded at 44,100 samples per second. Each sample contains data for a left and right channel, which may be considered to be a 2-vector (since CDs are recorded in stereo).
• Pictures. A picture assigns a color value to each of a set of points. Since the points lie on a plane, the domain is two-dimensional. If the picture is a physical object, such as a painting, it's a continuous signal. If the picture a digital image, it's a discrete signal. It's often convenient to represent color as the sum of the intensities of three primary colors, so that the signal is vector-valued with dimension three.
• Videos. A video signal is a sequence of images. A point in a video is identified by its position (two-dimensional) 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 a straightforward 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 the techniques of electrophysiology.

Motion involves change in position, such as this perspective of rapidly leaving Yongsan Station In physics, motion means a change in the position of a body relative to a reference point, as measured by a particular observer in a particular frame of reference. ... Space has been an interest for philosophers and scientists for much of human history, and hence it is difficult to provide an uncontroversial and clear definition outside of specific defined contexts. ... A schematic representation of hearing. ... Oscillation is the periodic variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ... Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface. ... The Compact Disc logo was inspired by that of the previous Compact Cassette. ... Look up second in Wiktionary, the free dictionary. ... Symbol for stereo Stereophonic sound, commonly called stereo, is the reproduction of sound, using two independent audio channels, through a pair of widely separated speaker systems, in such a way as to create a pleasant and natural impression of sound heard from various directions as in natural hearing. ... For images in Wikipedia, see Wikipedia:Images. ... A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. ... Primary Colors, a 1996 novel by Anonymous (later revealed by Donald Foster to be journalist Joe Klein), is a roman Ã  clef about U.S. President Bill Clintons first presidential campaign in 1992. ... Video is the technology of capturing, recording, processing, transmitting, and reconstructing moving pictures, typically using celluloid film, electronic signals, or digital media, primarily for viewing on television or computer monitors. ... A scanline is a line on a CRT tube, made up of dots. ... Membrane potential (or transmembrane potential or transmembrane potential difference or transmembrane potential gradient), is the electrical potential difference (voltage) across a cells plasma membrane. ... It has been suggested that this article or section be merged with Electrophysiology. ... Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ... Cells in culture, stained for keratin (red) and DNA (green). ... Schematic of typical animal cell, showing subcellular components. ... Drawing by Santiago RamÃ³n y Cajal of cells in the pigeon cerebellum. ... Electrophysiology is the study of the electrical properties of biological cells and tissues. ...

## Frequency analysis

Main article: Frequency domain

It is remarkably useful to analyze the frequency spectrum of a signal. This technique is applicable to all signals, both continuous and discrete. For instance, if a signal is passed through an LTI system, the frequency spectrum of the resulting output signal is the product of the frequency spectrum of the original input signal and the frequency response of the system. Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ... Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. ... Linear time invarient systems are called as lti systems it should satisify both linearity and time invarient quality. ... Frequency response is the measure of any systems response to frequency, but is usually used in connection with electronic amplifiers and similar systems, particularly in relation to audio signals. ...

## Entropy

Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or information content. Entropy of a Bernoulli trial as a function of success probability, often called the binary entropy function. ...

## See also

In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector. ... The phrase signal-to-noise ratio, often abbreviated SNR or S/N, is an engineering term for the ratio between the magnitude of a signal (meaningful information) and the magnitude of background noise. ... Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ... Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. ... It has been suggested that digital image processing be merged into this article or section. ... It has been suggested that this article or section be merged into image processing. ...

## Works cited

Shannon, C. E., 2005 , "A Mathematical Theory of Communication," (corrected reprint), accessed Dec. 15, 2005. Orig. 1948, Bell System Technical Journal, vol. 27, pp. 379-423, 623-656.

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