Perturbation Analysis of Discrete-Time Wilson Frames

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DOI: https://doi.org/10.28924/2291-8639-24-2026-168
Published: May 29, 2026
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Teena Kohli, Poonam Mantry, Amita Aggarwal, Perturbation Analysis of Discrete-Time Wilson Frames, Int. J. Anal. Appl., 24 (2026), 168.

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Teena Kohli, Poonam Mantry, Amita Aggarwal

Abstract

In this paper, we study the effect of perturbations of the generators on discrete-time Wilson frames (DTWFs) for l2(Z). We find that if the original system forms a DTWF and the perturbed system, obtained by adding another pair of generators in l2(Z), is a discrete-time Wilson Bessel sequence, then the system generated by the additive component alone is also a discrete-time Wilson Bessel sequence. Moreover, a sufficient condition under which the system corresponding to the additive component constitutes a DTWF is derived. Finally, we study discrete-time Wilson systems generated by finite linear combinations of DTWF generators and establish necessary and sufficient conditions for such systems to form DTWFs.

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