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Twisted Shift-Invariant System in L<sup>2</sup>(â„ <sup>2N</sup>)
Date Issued
01-01-2023
Author(s)
Das, Santi Ranjan
Velsamy, Rabeetha
Ramakrishnan, R. A.D.H.A.
Abstract
We consider a general twisted shift-invariant system, <![CDATA[ $V^{t}(\mathcal {A})$ ]]>, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system <![CDATA[ $V^{t}(\mathcal {A})$ ]]> to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.