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Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''
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'', 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'' b ...
,
images 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 ...
, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals,
subjective video quality Subjective video quality is video quality as experienced by humans. It is concerned with how video is perceived by a viewer (also called "observer" or "subject") and designates their opinion on a particular video sequence. It is related to the fiel ...
and to also detect or pinpoint components of interest in a measured signal.


History

According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical
numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...
techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948,
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Inst ...
wrote the influential paper "
A Mathematical Theory of Communication "A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in ''Bell System Technical Journal'' in 1948. It was renamed ''The Mathematical Theory of Communication'' in the 1949 book of the same name, a sma ...
" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission. Signal processing matured and flourished in the 1960s and 1970s, and digital signal processing became widely used with specialized digital signal processor chips in the 1980s.


Categories


Analog

Analog signal processing is for signals that have not been digitized, as in most 20th-century
radio 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 transmi ...
, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, passive filters,
active filter An active filter is a type of analog circuit implementing an electronic filter using active components, typically an amplifier. Amplifiers included in a filter design can be used to improve the cost, performance and predictability of a filter. ...
s, additive mixers, integrators, and delay lines. Nonlinear circuits include
compandor In telecommunication and signal processing, companding (occasionally called compansion) is a method of mitigating the detrimental effects of a channel with limited dynamic range. The name is a portmanteau of the words compressing and expanding, ...
s, multipliers (
frequency mixer In electronics, a mixer, or frequency mixer, is an electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals are applied to a mixer, and it produces new signals at the sum and di ...
s, voltage-controlled amplifiers),
voltage-controlled filter A voltage-controlled filter (VCF) is an electronic filter whose operating characteristics (primarily cutoff frequency) can be set by an input control voltage. Voltage controlled filters are widely used in synthesizers. A music synthesizer VCF a ...
s,
voltage-controlled oscillator A microwave (12–18GHz) voltage-controlled oscillator A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillat ...
s, and
phase-locked loop A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...
s.


Continuous time

Continuous-time signal processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points). The methods of signal processing include
time domain Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the c ...
,
frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a s ...
, and complex frequency domain. This technology mainly discusses the modeling of linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals


Discrete time

Discrete-time signal processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude. ''Analog discrete-time signal processing'' is a technology based on electronic devices such as sample and hold circuits, analog time-division
multiplexer In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The sel ...
s,
analog delay line An analog delay line is a network of electrical components connected in cascade, where each individual element creates a time difference between its input and output. It operates on analog signals whose amplitude varies continuously. In the c ...
s and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals. The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.


Digital

Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are
circular buffer In computer science, a circular buffer, circular queue, cyclic buffer or ring buffer is a data structure that uses a single, fixed-size buffer as if it were connected end-to-end. This structure lends itself easily to buffering data streams. Ther ...
s and lookup tables. Examples of algorithms are the fast Fourier transform (FFT),
finite impulse response In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of ''finite'' duration, because it settles to zero in finite time. This is in contrast to infinite impulse ...
(FIR) filter,
Infinite impulse response Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) which does not become exactly zero past a certain point, but continues indefinitely. This is in ...
(IIR) filter, and adaptive filters such as the Wiener and
Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
s.


Nonlinear

Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains. Nonlinear systems can produce highly complex behaviors including bifurcations,
chaos Chaos or CHAOS may refer to: Arts, entertainment and media Fictional elements * Chaos (''Kinnikuman'') * Chaos (''Sailor Moon'') * Chaos (''Sesame Park'') * Chaos (''Warhammer'') * Chaos, in ''Fabula Nova Crystallis Final Fantasy'' * Cha ...
,
harmonics A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', ...
, and subharmonics which cannot be produced or analyzed using linear methods. Polynomial signal processing is a type of non-linear signal processing, where
polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example ...
systems may be interpreted as conceptually straight forward extensions of linear systems to the non-linear case.


Statistical

Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. Statistical techniques are widely used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, and construct techniques based on this model to reduce the noise in the resulting image.


Application fields

*
Audio signal processing Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves— longitudinal waves which travel through air, consist ...
for electrical signals representing sound, such as speech or music * Image processing in digital cameras, computers and various imaging systems * Video processing for interpreting moving pictures *
Wireless communication Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most ...
waveform generations, demodulation, filtering, equalization * Control systems *
Array processing Array processing is a wide area of research in the field of signal processing that extends from the simplest form of 1 dimensional line arrays to 2 and 3 dimensional array geometries. Array structure can be defined as a set of sensors that are sp ...
for processing signals from arrays of sensors * Process control a variety of signals are used, including the industry standard 4-20 mA
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 d ...
*
Seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
* Financial signal processing analyzing financial data using signal processing techniques, especially for prediction purposes. *
Feature extraction In machine learning, pattern recognition, and image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning a ...
, such as image understanding and
speech recognition Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the ...
. * Quality improvement, such as noise reduction, image enhancement, and
echo cancellation Echo suppression and echo cancellation are methods used in telephony to improve voice quality by preventing echo from being created or removing it after it is already present. In addition to improving subjective audio quality, echo suppression ...
. * Source coding including audio compression, image compression, and video compression. * Genomic signal processing In communication systems, signal processing may occur at: * OSI layer 1 in the seven layer OSI model, the physical layer ( modulation, equalization, multiplexing, etc.); * OSI layer 2, the
data link layer The data link layer, or layer 2, is the second layer of the seven-layer OSI model of computer networking. This layer is the protocol layer that transfers data between nodes on a network segment across the physical layer. The data link layer ...
( forward error correction); * OSI layer 6, the
presentation layer In the seven-layer OSI model of computer networking, the presentation layer is layer 6 and serves as the data translator for the network. It is sometimes called the syntax layer. Description Within the service layering semantics of the OSI netw ...
(source coding, including
analog-to-digital conversion 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 provi ...
and
data compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressio ...
).


Typical devices

* Filters for example analog (passive or active) or digital ( FIR, IIR, frequency domain or stochastic filters, etc.) * Samplers and
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 ...
s for signal acquisition and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof. * Signal compressors * Digital signal processors (DSPs)


Mathematical methods applied

* Differential equations *
Recurrence relation In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
s * Transform theory * Time-frequency analysis for processing non-stationary signals * Spectral estimation for determining the spectral content (i.e., the distribution of power over frequency) of a time series *
Statistical signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
analyzing and extracting information from signals and noise based on their stochastic properties * Linear time-invariant system theory, and transform theory * Polynomial signal processing analysis of systems which relate input and output using polynomials * System identification and classification *
Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
* Complex analysis *
Vector spaces In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...
and
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 ...
*
Functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
*
Probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
and stochastic processes * Detection theory * Estimation theory *
Optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
* Numerical methods * Time series * Data mining for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns


See also

* Algebraic signal processing * Audio filter *
Bounded variation In mathematical analysis, a function of bounded variation, also known as ' function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a conti ...
*
Digital image processing Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allo ...
*
Dynamic range compression Dynamic range compression (DRC) or simply compression is an audio signal processing operation that reduces the volume of loud sounds or amplifies quiet sounds, thus reducing or ''compressing'' an audio signal's dynamic range. Compression is ...
,
companding In telecommunication and signal processing, companding (occasionally called compansion) is a method of mitigating the detrimental effects of a channel with limited dynamic range. The name is a portmanteau of the words compressing and expanding ...
,
limiting In electronics, a limiter is a circuit that allows signals below a specified input power or level to pass unaffected while attenuating (lowering) the peaks of stronger signals that exceed this threshold. Limiting is a type of dynamic range comp ...
, and noise gating * Fourier transform * Information theory *
Least-squares spectral analysis Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally ...
* Non-local means * Reverberation * Time series


References


Further reading

* * * * Kainam Thomas Won

Statistical Signal Processing lecture notes at the University of Waterloo, Canada. * Ali H. Sayed, Adaptive Filters, Wiley, NJ, 2008, . * Thomas Kailath, Ali H. Sayed, and
Babak Hassibi Babak Hassibi ( fa, بابک حسیبی, born in Tehran, Iran) is an Iranian-American electrical engineer, computer scientist, and applied mathematician who is the inaugural Mose and Lillian S. Bohn Professor of Electrical Engineering and Compu ...
, Linear Estimation, Prentice-Hall, NJ, 2000, .


External links


Signal Processing for Communications
– free online textbook by Paolo Prandoni and Martin Vetterli (2008)
Scientists and Engineers Guide to Digital Signal Processing
– free online textbook by Stephen Smith {{Authority control Mass media technology Telecommunication theory