"Construction of pairwise orthogonal Parseval frames generated by filters on LCA groups"Navneet, NavneetThe generalized translation invariant (GTI) systems unify the discrete frame theory of generalized shift-invariant systems with its continuous version, such as wavelets, shearlets, Gabor transforms, and others. This article provides sufficient conditions to construct pairwise orthogonal Parseval GTI frames in $L^2(G)$ satisfying the local integrability condition (LIC) and having the Calder\'on sum one, where $G$ is a second countable locally compact abelian group. The pairwise orthogonality plays a crucial role in multiple access communications, hiding data, synthesizing superframes and frames, etc. Further, we propose algorithms for constructing $N$ numbers of GTI Parseval frames, which are pairwise orthogonal. Consequently, we obtain an explicit construction of pairwise orthogonal Parseval frames in $L^2(\mathbb{R})$ and $L^2(G)$, using B-splines as a generating function. In the end, the results are particularly discussed for wavelet systems. |
| https://ps-mathematik.univie.ac.at/e/talks/strobl24_Navneet_2023-12_Abstract_Navneet1.pdf |
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