Frame bounds and discretization error of the 1-D Gabor transform

Ludek Klimes

Summary

Discrete Gabor functions used for the Gabor transform form a frame. Approximate analytic expressions for the frame bounds of this frame are derived. These expressions can be used to study analytically both the discretization error of the continuous Gabor transform and the stability of the discrete Gabor transform in dependence on the phase-space lattice intervals.

Keywords

Gabor function, Gabor transform, frame bounds, discretization error.

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In: Seismic Waves in Complex 3-D Structures, Report 18, pp. 95-108, Dep. Geophys., Charles Univ., Prague, 2008.
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