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Gabor frames in \(l^2 (\mathbb Z)\) from Gabor frames in \(L^2 (\mathbb{R})\). (English) Zbl 1457.42048

Summary: In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from \(L^2 (\mathbb R)\) to \(l^2 (\mathbb Z)\) maps Gabor frame in \(L^2 (\mathbb R)\) to a Gabor frame in \(l^2 (\mathbb Z)\).

MSC:

42C15 General harmonic expansions, frames
47B90 Operator theory and harmonic analysis
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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