Construction of pairwise orthogonal Parseval frames generated by filters on LCA groups

The 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 & oacute;n 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 provide a result 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(R) and L-2(G), using B-splines as a generating function. In the end, the results are particularly discussed for wavelet systems.