Rational time-frequency oblique dual Gabor frames based on the direct sum decomposition of <i> L ² </i> (ℝ)

The oblique dual frames overcome the limitations of traditional dual frames through direct sum decomposition of spaces, and provide a more flexible approach to signal reconstruction. This paper addresses oblique dual Gabor frame theory. We give a characterization of Gabor system-based direct sum decomposition of L 2 (ℝ). Based on this, using our Zak transform matrix techniques we characterize the oblique dual Gabor frame pairs, and present a parametric expression and a uniqueness characterization of the oblique dual Gabor frames for a given subspace Gabor frame. Some examples are also provided to illustrate the generality of our theory.