Towards a General Description of Translation-Invariant and Translation-Covariant Linear Transformations: A Natural Justification of Fourier Transforms and Fuzzy Transforms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F11%3AA12012L3" target="_blank" >RIV/61988987:17610/11:A12012L3 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Towards a General Description of Translation-Invariant and Translation-Covariant Linear Transformations: A Natural Justification of Fourier Transforms and Fuzzy Transforms
Original language description
In many practical situations, we are interested in the dependencies that do not change with time, i.e., that do not change when we change the origin of the time axis. The corresponding translation-invariant transformations are easy to describe: they correspond to convolutions, or, equivalently, to fuzzy transforms. It turns out that if we relax the invariance condition and require only that the transformation be translation-covariant (i.e., that it appropriately changes under translation), we get exactly two classes of transformations: Fourier transforms and fuzzy transforms. This result explain why both transforms have been successfully used in data processing.
Czech name
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Czech description
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of 2011 IFSA World Vongress - AFSS INternational Conference
ISBN
978-602-99359-0-5
ISSN
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e-ISSN
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Number of pages
6
Pages from-to
2111-2116
Publisher name
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Place of publication
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Event location
Surabya
Event date
Jun 21, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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