Discretized Gabor Frames of Totally Positive Functions

2013/08/13 by Severin Bannert, Karlheinz Gröchenig, Bannert, Severin +3
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1308.2808

openalex publication_date 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every undercritical rectangular lattice generates a Riesz sequence.

Citations

• The wavelet transform, time-frequency localization and signal analysis
• Some Weyl-Heisenberg frame bound calculations
• Hyperbolic Secants Yield Gabor Frames

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