Editing Signal processing (section)

==Categories==

===Analog===
{{main|Analog signal processing}}

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 filter]]s, [[active filter]]s, [[Electronic mixer|additive mixers]], [[integrator]]s, and [[Analog delay line|delay line]]s. Nonlinear circuits include [[compandor]]s, multipliers ([[frequency mixer]]s, [[voltage-controlled amplifier]]s), [[voltage-controlled filter]]s, [[voltage-controlled oscillator]]s, and [[phase-locked loop]]s.

===Continuous time===
[[Continuous signal|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

<math>
y(t) = \int_{-\infty}^\infty h(\tau) x(t - \tau) \, d\tau
</math>

In some contexts, <math>h(t)</math> 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 [[multiplexer]]s, [[analog delay line]]s and [[analog feedback shift register]]s. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.<ref>{{cite web |url=https://microwavelab.nd.edu/research/analog-signal-processing/ |title=Microwave & Millimeter-wave Circuits and Systems |access-date=2024-10-20}}</ref>

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===
{{main|Digital signal processing}}

Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose [[computer]]s or by digital circuits such as [[ASIC]]s, [[field-programmable gate array]]s or specialized [[digital signal processor]]s. Typical arithmetical operations include [[Fixed-point arithmetic|fixed-point]] and [[floating-point]], real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are [[circular buffer]]s and [[lookup table]]s. Examples of algorithms are the [[fast Fourier transform]] (FFT), [[finite impulse response]] (FIR) filter, [[Infinite impulse response]] (IIR) filter, and [[adaptive filter]]s such as the [[Wiener filter|Wiener]] and [[Kalman filter]]s.

===Nonlinear===
Nonlinear signal processing involves the analysis and processing of signals produced from [[nonlinear system]]s and can be in the time, [[frequency]], or spatiotemporal domains.<ref name="Billings">{{cite book |last=Billings |first=S. A. |title=Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains |publisher=Wiley |year=2013 |isbn=978-1-119-94359-4 }}</ref><ref name="VSA">{{cite book |author=Slawinska, J. |author2=Ourmazd, A. |author3=Giannakis, D. |title=2018 IEEE Statistical Signal Processing Workshop (SSP) |chapter=A New Approach to Signal Processing of Spatiotemporal Data |pages=338–342 |publisher=IEEE Xplore |year=2018 |doi=10.1109/SSP.2018.8450704|isbn=978-1-5386-1571-3 |s2cid=52153144 }}</ref> Nonlinear systems can produce highly complex behaviors including [[bifurcation theory|bifurcations]], [[chaos theory|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.<ref>{{cite book |author1=V. John Mathews |author2=Giovanni L. Sicuranza |title=Polynomial Signal Processing |date=May 2000 |isbn=978-0-471-03414-8 |publisher=Wiley}}</ref>

===Statistical ===
'''Statistical signal processing''' is an approach which treats signals as [[stochastic process]]es, utilizing their [[statistical]] properties to perform signal processing tasks.<ref name ="Scharf">{{cite book |first=Louis L. |last=Scharf |title=Statistical signal processing: detection, estimation, and time series analysis |publisher=[[Addison–Wesley]] |location=[[Boston]] |year=1991 |isbn=0-201-19038-9 |oclc=61160161}}</ref> 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 [[noise reduction|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.<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|url=https://ieeexplore.ieee.org/document/9043719|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|url=https://ieeexplore.ieee.org/document/10465260|last1=Fascista|first1=A.|last2=Coluccia|first2=A.|last3=Ravazzi|first3=C.|volume=10 |pages=277–293 |doi=10.1109/TSIPN.2024.3375593 |url-access=subscription}}</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|url=https://ieeexplore.ieee.org/document/9730033|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 }}</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|chapter-url=https://ieeexplore.ieee.org/document/9190887|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|chapter-url=https://ieeexplore.ieee.org/document/9412999|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>