Refine
Has Fulltext
- yes (91) (remove)
Document Type
- Conference Proceeding (38)
- Doctoral Thesis (16)
- Part of a Book (10)
- Article (8)
- Bachelor Thesis (8)
- Master's Thesis (3)
- Book (2)
- Periodical (2)
- Study Thesis (2)
- Habilitation (1)
Institute
- Graduiertenkolleg 1462 (19)
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (19)
- Universitätsbibliothek (11)
- Professur Bauphysik (8)
- Professur Informatik in der Architektur (6)
- F. A. Finger-Institut für Baustoffkunde (FIB) (4)
- Institut für Strukturmechanik (ISM) (4)
- An-Institute (2)
- Institut für Europäische Urbanistik (2)
- Professur Bauchemie und Polymere Werkstoffe (2)
- Geschichte und Theorie der Visuellen Kommunikation (1)
- Institut für Bauinformatik, Mathematik und Bauphysik (IBMB) (1)
- Junior-Professur Computational Architecture (1)
- Junior-Professur Psychophysiologie und Wahrnehmung (1)
- Professur Angewandte Mathematik (1)
- Professur Baubetrieb und Bauverfahren (1)
- Professur Baumechanik (1)
- Professur Content Management und Webtechnologien (1)
- Professur Entwerfen und Baugestaltung (1)
- Professur Grundbau (1)
- Professur Informatik im Bauwesen (1)
- Professur Medienmanagement (1)
- Professur Medienphilosophie (1)
- Professur Soziologie und Sozialgeschichte der Stadt (1)
- Professur Stahlbau (1)
- Professur Stochastik und Optimierung (1)
- Professur Theorie und Geschichte der modernen Architektur (1)
- Professur Tragwerkslehre (1)
Keywords
- Angewandte Informatik (36)
- Angewandte Mathematik (36)
- Computerunterstütztes Verfahren (36)
- Elektronisches Buch (7)
- Bauphysik (3)
- Bibliothek (3)
- E-Book-Reader (3)
- Urheberrecht (3)
- Architektur (2)
- Beton (2)
Year of publication
- 2012 (91) (remove)
We briefly review and use the recent comprehensive research on the manifolds of square roots of −1 in real Clifford geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the complex imaginary unit j is replaced by a square root of −1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs, which replaced the complex imaginary unit j only by blades (usually pseudoscalars) squaring to −1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w -shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem.