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===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-accessbibcode=subscription2024ITSIP..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|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 |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|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>
|title=Optimization of data-driven filterbank for automatic speaker verification
|journal=Digital Signal Processing |date=September 2020 |volume=104
|pagearticle-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
* [[Video processing]]{{spaced ndash}} for interpreting moving pictures
* 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]]).
===Underwater Signal Processing===
Underwater signal processing is essential for effective communication, sensing, and navigation in the ocean’s complex acoustic environment. A central component of this ___domain is sonar array processing, which harnesses the spatial diversity provided by arrays of sensors to improve signal detection and estimation under challenging conditions.
Sonar array processing plays a critical role in underwater communication and sensing by exploiting spatial diversity to enhance signal estimation in challenging acoustic environments. Sonar systems—particularly when equipped with arrays of vector and scalar sensors—can form directional beams and spatial filters to isolate desired signals while suppressing noise and interference from undesired directions. This spatial filtering capability is essential in time-spreading distortion channels, where multipath propagation from the sea surface, seabed, and various underwater obstacles causes significant signal degradation.
Multichannel array processing techniques utilize both scalar pressure measurements and particle velocity information provided by vector sensors to improve angular resolution and signal-to-noise ratio (SNR) in environments with severe multipath and noise interference <ref>R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou. 2024. "Multichannel signal detection in time-spreading distortion underwater channels using vector and scalar sensors: Theory and experiments." IEEE J. Oceanic Engineering, vol. 49, pp. 1151–1159.</ref>. The addition of particle velocity components significantly enhances spatial discrimination, allowing for better signal localization and estimation in both active and passive sonar modes <ref>E. Zhang. 2023. "Particle velocity underwater data communication: Physics, channels, system and experiments." IEEE Journal of Oceanic Engineering, vol. 48, pp. 1338–1347.</ref>, <ref>R. Rashid. 2023. "Underwater acoustic signal acquisition and sensing using a ring vector sensor communication receiver: Theory and experiments." Sensors, vol. 23, issue 6917.</ref>, <ref>R. Rashid. 2024. "On the performance of a new wireless communication compact multichannel underwater receiver using a sphere vector sensor." IEEE Transactions on Vehicular Technology, vol. 73, pp. 1458–1461.</ref>.
In passive sonar applications, array processing supports the detection and classification of weak signals generated by marine sources or stealth targets. When combined with advanced estimation methods like dictionary learning, array systems can blindly extract signal features even in unknown environments with complex propagation effects <ref>Rami Rashid, Ali Abdi, and Zoi-Heleni Michalopoulou. 2025. "Blind weak signal detection via dictionary learning in time-spreading distortion channels using vector sensors." JASA Express Letters, vol. 5, 064803.</ref>, <ref>Rami Rashid, Ali Abdi, and Zoi-Heleni Michalopoulou. 2024. "Blind passive signal detection via dictionary learning in unknown multipath time-spreading distortion underwater channels." J. Acoust. Soc. Am., vol. 155, A84.</ref>.
Experimental results reinforce the effectiveness of sonar array processing using multichannel vector sensor receivers and MIMO configurations. These systems have demonstrated high-performance underwater signal acquisition and data transmission in real-world conditions, leveraging spatial diversity and adaptive processing algorithms to overcome time-spreading distortion and noise <ref>E. Zhang, R. Rashid, and A. Abdi. 2023. "Underwater communication experiments for transmitting multiple data streams using a vector acoustic MIMO system: OFDM and FSK modulations." In Proc. MTS/IEEE Oceans, Biloxi, MS, pp. 1–5.</ref>, <ref>E. Zhang, R. Rashid, and A. Abdi. 2023. "Experiments on a compact multichannel vector sensor receiver for signal acquisition in underwater communication systems." In Proc. MTS/IEEE Oceans, Biloxi, MS, pp. 1–4.</ref>, <ref>R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou. 2022. "Theoretical and experimental multi-sensor signal detection in time spreading distortion underwater channels." In Proc. MTS/IEEE Oceans, Hampton Roads, VA, pp. 1–4.</ref>, <ref>Z. Qi, R. Rashid, A. Abdi, and D. Pompili. 2025. "Carrier frequency offset compensation for OSDM in underwater acoustic communications: Theory and experiments using a vector MIMO modem." In Proc. Conf. Inform. Sci. Syst., Johns Hopkins University, Baltimore, MD, pp. 1–6.</ref>.
In summary, sonar array processing forms the backbone of modern underwater signal processing, offering robust techniques to mitigate distortion, enhance SNR, and enable reliable communication and sensing in dynamic and multipath-rich underwater environments.
==Typical devices ==
* [[Reverberation]]
* [[Sensitivity (electronics)]]
* [[Similarity (signal processing)]]<!--[[User:Kvng/RTH]]-->
==References==
* {{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}}
* Kainam Thomas Wong [http://www.eie.polyu.edu.hk/~enktwong/]: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.
* [[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}}.<!--[[User:Kvng/RTH]]-->
==External links==
* [https://www.sp4comm.org/ Signal Processing for Communications] – free online textbook by Paolo Prandoni and Martin Vetterli (2008)
* [httphttps://www.dspguide.com Scientists and Engineers Guide to Digital Signal Processing] – free online textbook by Stephen Smith
* [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)
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