The Abc-Problem For Gabor Systems And Uniform Sampling In Shift-Invariant Spaces

Keywords

Gabor frame; Infinite matrix; Sampling; Shift-invariant space; Uniform stability

Abstract

In this chapter, we identify ideal window functions χI on finite intervals I and time–frequency shift lattices aℤ × bℤ such that the corresponding Gabor systems (Formula presented) are frames for L2(ℝ). Also we consider a stable recovery of rectangular signals f in a shift-invariant space (Formula presented) from their equally-spaced samples f(t0 + µ), µ ϵ aℤ, for arbitrary initial sampling position t0.

Publication Date

1-1-2015

Publication Title

Applied and Numerical Harmonic Analysis

Issue

9783319132297

Number of Pages

177-194

Document Type

Article; Book Chapter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-3-319-13230-3_8

Socpus ID

84989922230 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84989922230

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