TY - CHAP
A1 - Markwardt, Klaus
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - WAVELET ANALYSIS AND FREQUENCY BAND DECOMPOSITIONS
N2 - In many applications such as parameter identification of oscillating systems in civil enginee-ring, speech processing, image processing and others we are interested in the frequency con-tent of a signal locally in time. As a start wavelet analysis provides a time-scale decomposition of signals, but this wavelet transform can be connected with an appropriate time-frequency decomposition. For instance in Matlab are defined pseudo-frequencies of wavelet scales as frequency centers of the corresponding bands. This frequency bands overlap more or less which depends on the choice of the biorthogonal wavelet system. Such a definition of frequency center is possible and useful, because different frequencies predominate at different dyadic scales of a wavelet decomposition or rather at different nodes of a wavelet packet decomposition tree. The goal of this work is to offer better algorithms for characterising frequency band behaviour and for calculating frequency centers of orthogonal and biorthogonal wavelet systems. This will be done with some product formulas in frequency domain. Now the connecting procedu-res are more analytical based, better connected with wavelet theory and more assessable. This procedures doesn’t need any time approximation of the wavelet and scaling functions. The method only works in the case of biorthogonal wavelet systems, where scaling functions and wavelets are defined over discrete filters. But this is the practically essential case, because it is connected with fast algorithms (FWT, Mallat Algorithm). At the end corresponding to the wavelet transform some closed formulas of pure oscillations are given. They can generally used to compare the application of different wavelets in the FWT regarding it’s frequency behaviour.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29895
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Nguyen, Manh Hung
A1 - Gürlebeck, Klaus
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
ED - Werner, Frank
T1 - ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of Möbius transformations only and that the Möbius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27833
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -
TY - CHAP
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 7 - 9 2009, Bauhaus-University Weimar
T1 - Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 7. bis 9.7. 2009, Bauhaus-Universität Weimar
N2 - From 7 till 9 July 2009, the 18th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering is going to take place at the Bauhaus University Weimar. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences to report on their results in research, development and practice and to discuss. The conference offers several topics. Plenary lectures and thematic sessions will take place under the chairmanship of the mentioned colleagues.
We invite architects, civil engineers, designers, computer scientists, engineers, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference.
KW - Computerunterstütztes Verfahren
KW - Architektur
KW - Angewandte Mathematik
KW - Angewandte Informatik
KW - Computer Science Models in Engineering
KW - Multiscale and Multiphysical Models
KW - Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20120105-14855
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
ER -
TY - CHAP
A1 - Bock, Sebastian
A1 - Gürlebeck, Klaus
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions
N2 - The contribution focuses on the development of a basic computational scheme that provides a suitable calculation environment for the coupling of analytical near-field solutions with numerical standard procedures in the far-field of the singularity. The proposed calculation scheme uses classical methods of complex function theory, which can be generalized to 3-dimensional problems by using the framework of hypercomplex analysis. The adapted approach is mainly based on the factorization of the Laplace operator EMBED Equation.3 by the Cauchy-Riemann operator EMBED Equation.3 , where exact solutions of the respective differential equation are constructed by using an orthonormal basis of holomorphic and anti-holomorphic functions.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29281
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -