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Singular Value Decomposition
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [sv]

Digital information och kommunikation genom digitala medier är ett växande område. E-post och andra kommunikationsmedel används dagligen över hela världen. Parallellt med att området växer så växer även intresset av att hålla informationen säker. Transmission via antenner är inom signalbehandling ett välkänt område. Transmission från en sändare till en mottagare genom fri rymd är ett vanligt exempel. I en tuff miljö som till exempel ett rum med reflektioner och oberoende elektriska apparater kommer det att finnas en hel del distorsion i systemet och signalen som överförs kan, på grund av systemets egenskaper och buller förvrängas.Systemidentifiering är ett annat välkänt begrepp inom signalbehandling. Denna avhandling fokuserar på systemidentifiering i en tuff miljö med okända system. En presentation ges av matematiska verktyg från den linjära algebran samt en tillämpning inom signalbehandling. Denna avhandling grundar sig främst på en matrisfaktorisering känd som Singular Value Decomposition (SVD). SVD’n används här för att lösa komplicerade matrisinverser och identifiera system.Denna avhandling utförs i samarbete med Combitech AB. Deras expertis inom signalbehandling var till stor hjälp när teorin praktiserades. Med hjälp av ett välkänt programmeringsspråk känt som LabView praktiserades de matematiska verktygen och kunde synkroniseras med diverse instrument som användes för att generera signaler och system.

Abstract [en]

Digital information transmission is a growing field. Emails, videos and so on are transmitting around the world on a daily basis. Along the growth of using digital devises there is in some cases a great interest of keeping this information secure.

In the field of signal processing a general concept is antenna transmission. Free space between an antenna transmitter and a receiver is an example of a system. In a rough environment such as a room with reflections and independent electrical devices there will be a lot of distortion in the system and the signal that is transmitted might, due to the system characteristics and noise be distorted.

System identification is another well-known concept in signal processing. This thesis will focus on system identification in a rough environment and unknown systems. It will introduce mathematical tools from the field of linear algebra and applying them in signal processing. Mainly this thesis focus on a specific matrix factorization called Singular Value Decomposition (SVD). This is used to solve complicated inverses and identifying systems.

This thesis is formed and accomplished in collaboration with Combitech AB. Their expertise in the field of signal processing was of great help when putting the algorithm in practice. Using a well-known programming script called LabView the mathematical tools were synchronized with the instruments that were used to generate the systems and signals.

Place, publisher, year, edition, pages
2012. , p. 24
Keywords [en]
SVD, Singular value decomposition, signal processing
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:lnu:diva-21481OAI: oai:DiVA.org:lnu-21481DiVA, id: diva2:549583
External cooperation
Combitech AB
Subject / course
Electrical Engineering
Educational program
Electrical Engineering Programme, 180 credits
Presentation
2012-06-13, 13:15 (English)
Uppsok
Technology
Supervisors
Examiners
Available from: 2012-09-05 Created: 2012-09-04 Last updated: 2012-09-05Bibliographically approved

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CiteExportLink to record
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