In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

We compare three types of coherent Riesz families (Gabor systems, Wilson bases, and wavelets) with respect to their perturbation stability under convolution with elements of a family of typical channel functions. This problem is of key relevance in the design of modulation signal sets for digital communication over time–invariant channels. Upper and lower bounds on the orthogonal perturbation a...

This paper will look at the connection of operators and frames respectively related sequences from different viewpoints. We will give a survey of the classification of frames and similar sequences by the properties of the associated operators. Furthermore an important part will be the investigation of how to find a matrix representation of operators with Bessel sequences, frames and Riesz bases...

We consider equidistant discrete splines S(j), j ∈ Z, which may grow as O(|j|s) as |j| → ∞. Such splines present a relevant tool for digital signal processing. The Zak transforms of Bsplines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation o...