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'''Signal processing''' is an [[electrical engineering]] subfield that focuses on analyzing, modifying and synthesizing ''[[signal]]s'', such as [[audio signal processing|sound]], [[image processing|images]], [[Scalar potential|potential fields]], [[Seismic tomography|seismic signals]], [[Altimeter|altimetry processing]], and [[scientific measurements]].<ref>{{cite journal|last=Sengupta|first=Nandini|author2=Sahidullah, Md|author3=Saha, Goutam|date=August 2016|title=Lung sound classification using cepstral-based statistical features|journal=Computers in Biology and Medicine|volume=75|issue=1|pages=118–129|doi=10.1016/j.compbiomed.2016.05.013|pmid=27286184}}</ref> Signal processing techniques are used to optimize transmissions, [[ | '''Signal processing''' is an [[electrical engineering]] subfield that focuses on analyzing, modifying and synthesizing ''[[signal]]s'', such as [[audio signal processing|sound]], [[image processing|images]], [[Scalar potential|potential fields]], [[Seismic tomography|seismic signals]], [[Altimeter|altimetry processing]], and [[scientific measurements]].<ref>{{cite journal|last=Sengupta|first=Nandini|author2=Sahidullah, Md|author3=Saha, Goutam|date=August 2016|title=Lung sound classification using cepstral-based statistical features|journal=Computers in Biology and Medicine|volume=75|issue=1|pages=118–129|doi=10.1016/j.compbiomed.2016.05.013|pmid=27286184}}</ref> Signal processing techniques are used to optimize transmissions, [[digital storage]] efficiency, correcting distorted signals, improve [[subjective video quality]], and to detect or pinpoint components of interest in a measured signal.<ref>{{cite book|title=Discrete-Time Signal Processing|author=Alan V. Oppenheim and Ronald W. Schafer|publisher=Prentice Hall|year=1989|isbn=0-13-216771-9|page=1}}</ref> | ||
==History== | ==History== | ||
| Line 50: | Line 50: | ||
== Definition of a signal == | == Definition of a signal == | ||
In signal processing, a signal is represented as a [[Function (mathematics)|function]] of time: <math>x(t)</math>, where this function is either<ref>Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9</ref> | |||
* deterministic (then one speaks of a deterministic signal) or | * deterministic (then one speaks of a deterministic signal) or | ||
* a path <math>(x_t)_{t \in T}</math>, a realization of a [[stochastic process]] <math>(X_t)_{t \in T}</math> | * a path <math>(x_t)_{t \in T}</math>, a realization of a [[stochastic process]] <math>(X_t)_{t \in T}</math> | ||
| Line 62: | Line 62: | ||
===Continuous time=== | ===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]], [[frequency domain]], and [[complex frequency|complex frequency domain]]. This technology mainly discusses the modeling of a [[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. For example, in time domain, a continuous-time signal <math>x(t)</math> passing through a [[linear time-invariant]] filter/system denoted as <math>h(t)</math>, can be expressed at the output as | The methods of signal processing include [[time domain]], [[frequency domain]], and [[complex frequency|complex frequency domain]]. This technology mainly discusses the modeling of a [[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. For example, in time domain, a continuous-time signal <math>x(t)</math> passing through a [[linear time-invariant]] filter/system denoted as <math>h(t)</math>, can be expressed at the output as | ||
| Line 93: | Line 93: | ||
===Graph === | ===Graph === | ||
'''Graph signal processing''' generalizes signal processing tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph.<ref name ="Ortega">{{cite book |first=A. |last=Ortega |title=Introduction to Graph Signal Processing |publisher=[[Cambridge University Press]] |location=[[Cambridge]] |year=2022 |isbn=9781108552349}}</ref> Graph signal processing presents several key points such as sampling signal techniques,<ref name="Tanaka">{{cite journal|title=Generalized Sampling on Graphs with Subspace and Smoothness Prior|journal=IEEE Transactions on Signal Processing|date=2020 | '''Graph signal processing''' generalizes signal processing tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph.<ref name ="Ortega">{{cite book |first=A. |last=Ortega |title=Introduction to Graph Signal Processing |publisher=[[Cambridge University Press]] |location=[[Cambridge]] |year=2022 |isbn=9781108552349}}</ref> Graph signal processing presents several key points such as sampling signal techniques,<ref name="Tanaka">{{cite journal|title=Generalized Sampling on Graphs with Subspace and Smoothness Prior|journal=IEEE Transactions on Signal Processing|date=2020|last1=Tanaka|first1=Y.|last2=Eldar|first2=Y.|volume=68 |pages=2272–2286 |doi=10.1109/TSP.2020.2982325 |arxiv=1905.04441 |bibcode=2020ITSP...68.2272T }}</ref> recovery techniques <ref name="Fascista">{{cite journal|title=Graph Signal Reconstruction under Heterogeneous Noise via Adaptive Uncertainty-Aware Sampling and Soft Classification|journal=IEEE Transactions on Signal and Information Processing over Networks|date=2024|last1=Fascista|first1=A.|last2=Coluccia|first2=A.|last3=Ravazzi|first3=C.|volume=10 |pages=277–293 |doi=10.1109/TSIPN.2024.3375593 |bibcode=2024ITSIP..10..277F }}</ref> and time-varying techiques.<ref name="Giraldo">{{cite journal|title=Reconstruction of Time-varying Graph Signals via Sobolev Smoothness|journal=IEEE Transactions on Signal and Information Processing over Networks|date=March 2022|last1=Giraldo|first1=J.|last2=Mahmood|first2=A. |last3=Garcia-Garcia|first3=B.|last4=Thanou|first4=D.|last5=Bouwmans|first5=T.|volume=8 |pages=201–214 |doi=10.1109/TSIPN.2022.3156886 |arxiv=2207.06439 |bibcode=2022ITSIP...8..201G }}</ref> Graph signal processing has been applied with success in the field of image processing, computer vision <ref name="Giraldo1">{{cite book|title=2020 IEEE International Conference on Image Processing (ICIP)|date=October 2020|last1=Giraldo|first1=J.|last2=Bouwmans|first2=T.|chapter= Semi-Supervised Background Subtraction of Unseen Videos: Minimization of the Total Variation of Graph Signals|pages= 3224–3228|doi= 10.1109/ICIP40778.2020.9190887|isbn= 978-1-7281-6395-6}}</ref> | ||
<ref name="Giraldo2">{{cite book|title=2020 25th International Conference on Pattern Recognition (ICPR)|date=2020 | <ref name="Giraldo2">{{cite book|title=2020 25th International Conference on Pattern Recognition (ICPR)|date=2020|last1=Giraldo|first1=J.|last2=Bouwmans|first2=T.|chapter=GraphBGS: Background Subtraction via Recovery of Graph Signals |pages=6881–6888 |doi=10.1109/ICPR48806.2021.9412999 |arxiv=2001.06404 |isbn=978-1-7281-8808-9 }}</ref> | ||
<ref name="Giraldo3">{{cite book|title=Frontiers of Computer Vision|date=February 2021|chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-81638-4_3|last1=Giraldo|first1=J.|last2=Javed|first2=S.|last3=Sultana|first3=M.|last4=Jung|first4=S.|last5=Bouwmans|first5=T.|chapter=The Emerging Field of Graph Signal Processing for Moving Object Segmentation |series=Communications in Computer and Information Science |volume=1405 |pages=31–45 |doi=10.1007/978-3-030-81638-4_3 |isbn=978-3-030-81637-7 }}</ref> and sound anomaly detection.<ref name="Bouwmans1">{{cite journal|title=Anomalous Sound Detection for Road Surveillance based on Graph Signal Processing|journal=European Conference on Signal Processing, EUSIPCO 2024|date=2024|url=https://ieeexplore.ieee.org/document/10715291|last1=Mnasri|first1=Z.|last2=Giraldo|first2=H. |last3=Bouwmans|first3=T.|pages=161–165 |doi=10.23919/EUSIPCO63174.2024.10715291 |isbn=978-9-4645-9361-7 }}</ref> | <ref name="Giraldo3">{{cite book|title=Frontiers of Computer Vision|date=February 2021|chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-81638-4_3|last1=Giraldo|first1=J.|last2=Javed|first2=S.|last3=Sultana|first3=M.|last4=Jung|first4=S.|last5=Bouwmans|first5=T.|chapter=The Emerging Field of Graph Signal Processing for Moving Object Segmentation |series=Communications in Computer and Information Science |volume=1405 |pages=31–45 |doi=10.1007/978-3-030-81638-4_3 |isbn=978-3-030-81637-7 }}</ref> and sound anomaly detection.<ref name="Bouwmans1">{{cite journal|title=Anomalous Sound Detection for Road Surveillance based on Graph Signal Processing|journal=European Conference on Signal Processing, EUSIPCO 2024|date=2024|url=https://ieeexplore.ieee.org/document/10715291|last1=Mnasri|first1=Z.|last2=Giraldo|first2=H. |last3=Bouwmans|first3=T.|pages=161–165 |doi=10.23919/EUSIPCO63174.2024.10715291 |isbn=978-9-4645-9361-7 }}</ref> | ||
| Line 103: | Line 103: | ||
|title=Optimization of data-driven filterbank for automatic speaker verification | |title=Optimization of data-driven filterbank for automatic speaker verification | ||
|journal=Digital Signal Processing |date=September 2020 |volume=104 | |journal=Digital Signal Processing |date=September 2020 |volume=104 | ||
| | |article-number=102795 |doi= 10.1016/j.dsp.2020.102795|arxiv=2007.10729|bibcode=2020DSP...10402795S |s2cid=220665533 }}</ref> | ||
* [[Image processing]]{{spaced ndash}} in digital cameras, computers and various imaging systems | * [[Image processing]]{{spaced ndash}} in digital cameras, computers and various imaging systems | ||
* [[Video processing]]{{spaced ndash}} for interpreting moving pictures | * [[Video processing]]{{spaced ndash}} for interpreting moving pictures | ||
| Line 148: | Line 148: | ||
*[[Optimization]]<ref name="PalomarEldar2010">{{cite book|author1=Daniel P. Palomar|author2=Yonina C. Eldar|title=Convex Optimization in Signal Processing and Communications|url=https://books.google.com/books?id=UOpnvPJ151gC|year=2010|publisher=Cambridge University Press|isbn=978-0-521-76222-9}}</ref> | *[[Optimization]]<ref name="PalomarEldar2010">{{cite book|author1=Daniel P. Palomar|author2=Yonina C. Eldar|title=Convex Optimization in Signal Processing and Communications|url=https://books.google.com/books?id=UOpnvPJ151gC|year=2010|publisher=Cambridge University Press|isbn=978-0-521-76222-9}}</ref> | ||
*[[Numerical methods]] | *[[Numerical methods]] | ||
*[[Data mining]]{{spaced ndash}} for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns | *[[Data mining]]{{spaced ndash}} 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== | ==See also== | ||
| Line 154: | Line 154: | ||
* [[Audio filter]] | * [[Audio filter]] | ||
* [[Bounded variation]] | * [[Bounded variation]] | ||
* [[Dynamic range compression]] | |||
* [[Dynamic range compression | |||
* [[Information theory]] | * [[Information theory]] | ||
* [[Least-squares spectral analysis]] | * [[Least-squares spectral analysis]] | ||
| Line 163: | Line 161: | ||
* [[Sensitivity (electronics)]] | * [[Sensitivity (electronics)]] | ||
* [[Similarity (signal processing)]] | * [[Similarity (signal processing)]] | ||
* [[Wiener filter]] | |||
==References== | ==References== | ||
| Line 171: | Line 170: | ||
* {{cite book|last=P Stoica|first=R Moses|title=Spectral Analysis of Signals|year=2005|publisher=Prentice Hall|location=NJ|url=https://user.it.uu.se/%7Eps/SAS-new.pdf}} | * {{cite book|last=P Stoica|first=R Moses|title=Spectral Analysis of Signals|year=2005|publisher=Prentice Hall|location=NJ|url=https://user.it.uu.se/%7Eps/SAS-new.pdf}} | ||
* {{cite book |first=Athanasios |last=Papoulis |title=Probability, Random Variables, and Stochastic Processes |year=1991 |edition=third |publisher=McGraw-Hill |isbn=0-07-100870-5}} | * {{cite book |first=Athanasios |last=Papoulis |title=Probability, Random Variables, and Stochastic Processes |year=1991 |edition=third |publisher=McGraw-Hill |isbn=0-07-100870-5}} | ||
* [[Ali H. Sayed]], Adaptive Filters, Wiley, NJ, 2008, {{isbn|978-0-470-25388-5}}. | * [[Ali H. Sayed]], Adaptive Filters, Wiley, NJ, 2008, {{isbn|978-0-470-25388-5}}. | ||
* [[Thomas Kailath]], [[Ali H. Sayed]], and [[Babak Hassibi]], Linear Estimation, Prentice-Hall, NJ, 2000, {{isbn|978-0-13-022464-4}}. | * [[Thomas Kailath]], [[Ali H. Sayed]], and [[Babak Hassibi]], Linear Estimation, Prentice-Hall, NJ, 2000, {{isbn|978-0-13-022464-4}}. | ||
* [https://sp4comm.org Signal Processing for Communications] – free online textbook by Paolo Prandoni and Martin Vetterli (2008) | |||
* [https://dspguide.com Scientists and Engineers Guide to Digital Signal Processing] – free online textbook by Stephen Smith | |||
==External links== | ==External links== | ||
* [https://www.dsprelated.com/freebooks/sasp/ Julius O. Smith III: Spectral Audio Signal Processing] – free online textbook | * [https://www.dsprelated.com/freebooks/sasp/ Julius O. Smith III: Spectral Audio Signal Processing] – free online textbook | ||
* [https://sites.google.com/view/gsp-website/graph-signal-processing Graph Signal Processing Website] – free online website by Thierry Bouwmans (2025) | * [https://sites.google.com/view/gsp-website/graph-signal-processing Graph Signal Processing Website] – free online website by Thierry Bouwmans (2025) | ||
{{DSP}} | {{DSP}} | ||
{{Authority control}} | {{Authority control}} | ||
Latest revision as of 17:22, 9 November 2025
Template:Short description Template:Redirect-distinguish Template:Multiple issues
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.[1] Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal.[2]
History
According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis 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.[3]
In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal.[4] The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.[5]
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.[5]
Definition of a signal
In signal processing, a signal is represented as a function of time: , where this function is either[6]
- deterministic (then one speaks of a deterministic signal) or
- a path , a realization of a stochastic process
Categories
Analog
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Analog signal processing is for signals that have not been digitized, as in most 20th-century radio, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators, and delay lines. Nonlinear circuits include compandors, multipliers (frequency mixers, voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators, and phase-locked loops.
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, frequency domain, and complex frequency domain. This technology mainly discusses the modeling of a 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. For example, in time domain, a continuous-time signal passing through a linear time-invariant filter/system denoted as , can be expressed at the output as
In some contexts, is referred to as the impulse response of the system. The above convolution operation is conducted between the input and the system.
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 multiplexers, analog delay lines 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.[7]
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
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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. 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 buffers and lookup tables. Examples of algorithms are the fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters.
Nonlinear
Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatiotemporal domains.[8][9] Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods.
Polynomial signal processing is a type of non-linear signal processing, where polynomial systems may be interpreted as conceptually straightforward extensions of linear systems to the nonlinear case.[10]
Statistical
Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.[11] 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.
Graph
Graph signal processing generalizes signal processing tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph.[12] Graph signal processing presents several key points such as sampling signal techniques,[13] recovery techniques [14] and time-varying techiques.[15] Graph signal processing has been applied with success in the field of image processing, computer vision [16] [17] [18] and sound anomaly detection.[19]
Application fields
- Audio signal processingTemplate:Spaced ndash for electrical signals representing sound, such as speech or music[20]
- Image processingTemplate:Spaced ndash in digital cameras, computers and various imaging systems
- Video processingTemplate:Spaced ndash for interpreting moving pictures
- Wireless communicationTemplate:Spaced ndash waveform generations, demodulation, filtering, equalization
- Control systems
- Array processingTemplate:Spaced ndash for processing signals from arrays of sensors
- Process controlTemplate:Spaced ndash a variety of signals are used, including the industry standard 4-20 mA current loop
- Seismology
- Feature extraction, such as image understanding, semantic audio and speech recognition.
- Quality improvement, such as noise reduction, image enhancement, and echo cancellation.
- Source coding including audio compression, image compression, and video compression.
- Genomic signal processing[21]
- In geophysics, signal processing is used to amplify the signal vs the noise within time-series measurements of geophysical data. Processing is conducted within the time domain or frequency domain, or both.[22][23]
In communication systems, signal processing may occur at:Script error: No such module "Unsubst".
- OSI layer 1 in the seven-layer OSI model, the physical layer (modulation, equalization, multiplexing, etc.);
- OSI layer 2, the data link layer (forward error correction);
- OSI layer 6, the presentation layer (source coding, including analog-to-digital conversion and data compression).
Typical devices
- FiltersTemplate:Spaced ndash for example analog (passive or active) or digital (FIR, IIR, frequency domain or stochastic filters, etc.)
- Samplers and analog-to-digital converters 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.
- Digital signal processors (DSPs)
Mathematical methods applied
- Differential equations[24]Template:Spaced ndash for modeling system behavior, connecting input and output relations in linear time-invariant systems. For instance, a low-pass filter such as an RC circuit can be modeled as a differential equation in signal processing, which allows one to compute the continuous output signal as a function of the input or initial conditions.
- Recurrence relations[25]
- Transform theory
- Time-frequency analysisTemplate:Spaced ndash for processing non-stationary signals[26]
- Linear canonical transformation
- Spectral estimationTemplate:Spaced ndash for determining the spectral content (i.e., the distribution of power over frequency) of a set of time series data points[27]
- Statistical signal processingTemplate:Spaced ndash analyzing and extracting information from signals and noise based on their stochastic properties
- Linear time-invariant system theory, and transform theory
- Polynomial signal processingTemplate:Spaced ndash analysis of systems which relate input and output using polynomials
- System identification[8] and classification
- Calculus
- Coding theory
- Complex analysis[28]
- Vector spaces and Linear algebra[29]
- Functional analysis[30]
- Probability and stochastic processes[11]
- Detection theory
- Estimation theory
- Optimization[31]
- Numerical methods
- Data miningTemplate:Spaced ndash 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
- Dynamic range compression
- Information theory
- Least-squares spectral analysis
- Non-local means
- Reverberation
- Sensitivity (electronics)
- Similarity (signal processing)
- Wiener filter
References
Further reading
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- Ali H. Sayed, Adaptive Filters, Wiley, NJ, 2008, Template:Isbn.
- Thomas Kailath, Ali H. Sayed, and Babak Hassibi, Linear Estimation, Prentice-Hall, NJ, 2000, Template:Isbn.
- 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
External links
- Julius O. Smith III: Spectral Audio Signal Processing – free online textbook
- Graph Signal Processing Website – free online website by Thierry Bouwmans (2025)
Template:DSP Template:Authority control
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- ↑ Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9
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