In the fields of communications Telecommunication is the transmission of messages, over significant distances, for the purpose of communication. In earlier times, telecommunications involved the use of visual signals, such as smoke, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded drumbeats, lung-blown horns, or sent by loud whistles, for, signal processing Signal processing is an area of electrical engineering, systems engineering, and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example, and in electrical engineering Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical power supply. It now covers a range of subtopics more generally, a signal is any time-varying or spatial-varying quantity.

In the physical world, any quantity Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time. For that reason, the changes in the physical quantities of a system describe its transformation measurable through time or over space can be taken as a signal. Within a complex society, any set of human information Information, in its most restricted technical sense, is an ordered sequence of symbols. As a concept, however, information has many meanings. Moreover, the concept of information is closely related to notions of constraint, communication, control, form, instruction, knowledge, meaning, mental stimulus, pattern, perception, and representation or machine data The term data refers to groups of information that represent the qualitative or quantitative attributes of a variable or set of variables. Data are typically the results of measurements and can be the basis of graphs, images, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which information and can also be taken as a signal. Such information or machine data (for example, the dots on a screen In digital imaging, a pixel is a single point in a raster image. The pixel is the smallest addressable screen element; it is the smallest unit of picture that can be controlled. Each pixel has its own address. The address of a pixel corresponds to its coordinates. Pixels are normally arranged in a 2-dimensional grid, and are often represented, the ink making up text on a paper page, or the words now flowing into the reader's mind) must all be part of systems existing in the physical world – either living or non-living.

Despite the complexity of such systems, their outputs and inputs can often be represented as simple quantities Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time. For that reason, the changes in the physical quantities of a system describe its transformation measurable through time or across space. In the latter half of the 20th century, electrical engineering Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical power supply. It now covers a range of subtopics itself separated into several disciplines, specializing in the design and analysis of physical signals and systems, on the one hand, and in the functional behavior and conceptual structure of the complex human and machine systems, on the other. These engineering disciplines have led the way in the design, study, and implementation of systems that take advantage of signals as simple measurable quantities Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time. For that reason, the changes in the physical quantities of a system describe its transformation in order to facilitate the transmission Data transmission, digital transmission or digital communications is the physical transfer of data over a point-to-point or point-to-multipoint transmission medium. Examples of such media are copper wires, optical fibres, wireless communication media, and storage media. The data is often represented as an electro-magnetic signal, such as an, storage A data storage device is a device for recording information (data). Recording can be done using virtually any form of energy, spanning from manual muscle power in handwriting, to acoustic vibrations in phonographic recording, to electromagnetic energy modulating magnetic tape and optical discs, and manipulation of information.

Some definitions

Definitions specific to subfields are common. For example, in information theory Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data. Since its inception it, a signal is a codified message, that is, the sequence of states in a communication channel that encodes a message.

In the context of signal processing Signal processing is an area of electrical engineering, systems engineering, and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example, arbitrary binary data streams are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

In a communication 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 , commonly referred to as a phone, is a telecommunications device that transmits and receives sound, most commonly the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to one another. It is one of the most common household. The telephone transmitter converts the sounds into an electrical voltage The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference (also called "electrostatic potential difference"). It is named in honor of the Italian physicist Alessandro Volta (1745–1827), who invented the signal. The signal is transmitted to the receiving telephone by wires; and at the receiver it is reconverted into sounds.

In telephone networks, signalling In the public switched telephone network , in-band signaling is the exchange of call control information within the same channel that the telephone call itself is using. An example is dual-tone multi-frequency signaling (DTMF), which is used on most telephone lines to customer premises, for example common channel signalling, 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 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 statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. Time series analysis comprises in other fields. Continuous-time signals are often referred to as continuous signals even when the signal functions are not continuous In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous". An intuitive though imprecise idea of continuity is; an example is a square-wave signal.

A second important distinction is between discrete-valued and continuous-valued. Digital signals The term digital signal is used to refer to more than one concept. It can refer to discrete-time signals that have a discrete number of levels, for example a sampled and quantified analog signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a are sometimes defined as discrete-valued sequencies of quantified values, that may or may not be derived from an underlying continuous-valued physical process. In other contexts, digital signals are defined as the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation In electronics, modulation is the process of varying one or more properties of high frequency periodic waveform, called the carrier signal, with respect to a modulating signal. This is done in a similar fashion as a musician may modulate a tone from a musical instrument by varying its volume, timing and pitch. The three key parameters of a method is considered as converted to an analog signal, while it is considered as a digital signal in the second case.

Discrete-time and continuous-time signals

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 In mathematics, the real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an (or complex A complex number is a number consisting of a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1. The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the) numbers.

A continuous-time real (or complex) signal is any real-valued (or complex-valued) function In mathematics, a function is a relation between a given set of elements and another set of elements (the codomain), which associates each element in the domain with exactly one element in the codomain. The elements so related can be any kind of thing (words, objects, qualities) but are typically mathematical quantities, such as real numbers 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 An Analog or analogue 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. It differs from a digital signal in terms of small fluctuations in the signal which are meaningful. Analog is usually thought of in an and digital The term digital signal is used, to refer to more than one concept. It can refer to discrete-time signals that have a discrete number of levels, for example a sampled and quantified analog signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a. In short, the difference between them is that digital signals are discrete and quantized, as defined below, while analog signals possess neither property.

Discretization

One of the fundamental distinctions between different types of signals is between continuous A continuous signal or a continuous-time signal is a varying quantity whose domain, which is often time, is a continuum (e.g., a connected interval of the reals). That is, the function's domain is an uncountable set. The function itself need not be continuous. To contrast, a discrete time signal has a countable domain, like the natural numbers and discrete time Discrete time is non-continuous time. Sampling at non-continuous times results in discrete-time samples. For example, a newspaper may report the price of crude oil once every 24 hours. In general, the sampling period in discrete-time systems is constant, but in some cases nonuniform sampling is also used. 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 (DT) signal is the set of integers The integers are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 6 (or some interval). What these integers represent depends on the nature of the signal.

DT signals often arise via sampling In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples (a discrete-time signal) of CT signals. An audio signal, for example consists of a continually fluxuating voltage on a line that can be digitized by an ADC An analog-to-digital converter is a device which converts continuous signals to discrete digital numbers. The reverse operation is performed by a digital-to-analog converter (DAC) circuit, wherein the circuit will read the voltage level on the line, say, every 50 µs. The resulting stream of numbers are stored as digital data on a discrete-time signal. Computers A computer is a programmable machine that receives input, stores and manipulates data//information, and provides output in a useful format and other digital A digital system is a data technology that uses discrete values. By contrast, non-digital (or analog) systems use a continuous range of values to represent information. Although digital representations are discrete, the information represented can be either discrete, such as numbers, letters or icons, or continuous, such as sounds, images, and devices are restricted to discrete time.

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 mathematics, a finite set is a set that has a finite number of elements. For example,; in other words, it is quantized In digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively small ("finite") set of ("values which can still take on continuous range") discrete symbols or integer values. For example, rounding a real number in the.

Examples of signals

• Motion In physics, motion is change of location or position of an object with respect to time. Change in motion is the result of an applied force. Motion is typically described in terms of velocity also seen as speed, acceleration, displacement, and time. An object's velocity cannot change unless it is acted upon by a force, as described by Newton's. The motion of a particle through some space Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines ' 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 Sound is a travelling wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations. Since a sound is a vibration Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation.& of a medium (such as air), a sound signal associates a pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure value to every value of time and three space coordinates. A microphone A microphone (colloquially called a mic or mike is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1876, Emile Berliner invented the first microphone used as a telephone voice transmitter. Microphones are used in many applications such as telephones, tape recorders, karaoke systems, hearing aids, 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 A Compact Disc is an optical disc used to store digital data. It was originally developed to store sound recordings exclusively, but later it also allowed the preservation of other types of data. Audio CDs have been commercially available since October 1982. In 2010, they remain the standard physical storage medium for audio (CDs). CDs contain discrete signals representing sound, recorded at 44,100 samples per second The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock. Each sample contains data for a left and right channel, which may be considered to be a 2-vector signal (since CDs are recorded in stereo Stereophonic sound, commonly called stereo, is the reproduction of sound using two or more independent audio channels through a symmetrical configuration of loudspeakers in such a way as to create the impression of sound heard from various directions, as in natural hearing. It is often contrasted with monophonic, or "mono" sound, where).
• Pictures An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person. 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 is a digital image A digital image is a representation of a two-dimensional image using ones and zeros . Depending on whether or not the image resolution is fixed, it may be of vector or raster type. Without qualifications, the term "digital image" usually refers to raster images also called bitmap images, it's a discrete signal. It's often convenient to represent color as the sum of the intensities of three primary colors Modern science has now demonstrated that the three primary colors are red, green, and blue; the three colors that correspond with the peak sensitivity of the three color photo-receptors in human eyes. These three colors can be combined to make nearly all colors perceivable by humans. The use of these colors can be observed in overlapping projected, so that the signal is vector-valued with dimension three.
• Videos Video is the technology of electronically capturing, recording, processing, storing, transmitting, and reconstructing a sequence of still images representing scenes in motion. 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.

Frequency analysis

Signals are often analyzed or modeled in terms of their frequency spectrum. Frequency domain techniques are applicable to all signals, both continuous-time and discrete-time. 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.

Entropy

Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or information content.

See also

• Impulse function
• Signal noise
• Signal to noise ratio
• Signal processing
  • Digital signal processing
• Image processing
  • Digital image processing
• Wikibook Signals and Systems

References

• Hsu, P. H. Schaum's Theory and Problems: Signals and Systems, McGraw-Hill 1995, ISBN 0-07-030641-9
• Lathi, B.P., Signal Processing & Linear Systems, Berkeley-Cambridge Press, 1998, ISBN 0-0941413-35-7
• Shannon, C. E., 2005 [1948], "A Mathematical Theory of Communication," (corrected reprint), accessed Dec. 15, 2005. Orig. 1948, Bell System Technical Journal, vol. 27, pp. 379–423, 623-656.

Categories: Digital signal processing | Signal processing

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