ICCHA2022

8th International Conference on
Computational Harmonic Analysis

September 12-16, 2022

Ingolstadt, Germany

"EXPLICIT CONSTRUCTION OF PAIRWISE ORTHOGONAL PARSEVAL FRAMES"

Navneet, Navneet

In this article, we construct an example of an orthogonal GSI Parseval frame for spaces L2(R) and L2(Z). In the conclusion of these two examples, we state the general result for the construction of the orthogonal GSI Parseval frame in L2(R). Then we generalize our results on the locally compact abelian group. We obtain conditions on the matrix of filter banks when two GTI frame pairs are orthogonal in the LCA group with the co-compact subgroup. We apply our characterization results to get a necessary and sufficient conditions pair of wavelets(as GTI systems) to be orthogonal in the LCA group. In particular, if G = R, to construct orthogonal wavelet pairs, we provide examples of frame generating functions and filter banks. After that, we obtain a general construction for arbitrarily many orthogonal GTI frame pairs in the context of LCA groups by using a paraunitary matrix. As a characterization of our result, we give an example of pair of orthogonal Parseval frames using the B-spline function as a frame generating function. The construction is then applied to synthesize GTI frame pairs over super-spaces.
http://univie.ac.at/projektservice-mathematik/e/talks/ICCHA2022_Navneet_2022-05_Untitled document-2.pdf

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