Gabor frames by sampling and periodization

By sampling the window of a Gabor frame for L2 (R) belonging to Feichtinger’s algebra, S0(R), one obtains a Gabor frame for l2 (Z). In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces L2 (R), l2 (Z), L2 ([0, L]) and CL . Some new results about general dual windows with respect to sampling and periodization are presented as well. This theory is used to show a new result of the Kaiblinger type to construct an approximation to the canonical dual window of a Gabor frame for L2 (R).

• Type: Journal
• Year: 2007
• Where: ADCM
• Authors: Peter L. Søndergaard
• Keywords: ADCM 2007, Dual Window, Gabor Frame, Window