Gabor frame

One may be interested in Gabor frames and its related theory if one looks further into the frame framework. First, denote a lattice by Λ=A2d, where A is an invertible matrix, and let π(ξ,ϕ)f=e2πiξxf(x-ϕ)


Let gL2(Rd) be a nonzero window, and let λΛ, then


is a Gabor system. If G(g,λ) is a frame, it’s called a Gabor frame for L2(Rd)

Supose now that one wants to look at a more general framework, and work with functions in L2(d,n). Then the definition above generalises to


Let 𝐠L2(Rd,Cn) be a nonzero window and let λΛ, then


is a Gabor super-frame if the frame inequalities hold, where


and for 𝐟,𝐡L2(Rd,Cn)



  • 1 Karlheinz Gröchenig, ”Foundations of Time-Frequency Analysis,” Birkhhäuser (2000)
Title Gabor frame
Canonical name GaborFrame
Date of creation 2013-03-22 17:08:28
Last modified on 2013-03-22 17:08:28
Owner ErlendA (6587)
Last modified by ErlendA (6587)
Numerical id 5
Author ErlendA (6587)
Entry type Definition
Classification msc 46C99
Defines Gabor frame
Defines Gabor super-frame
Defines Vector-valued Gabor frame