Phase Retrieval from Sampled Gabor Transform Magnitudes: Counterexamples

Abstract We consider the recovery of square-integrable signals from discrete, equidistant samples their Gabor transform magnitude and show that, in general, can not be recovered such samples. In particular, we that for any lattice, one construct functions $$L^2({\mathbb {R}})$$ L2(R) which do agree up to global phase but whose magnitudes sampled on lattice agree. These have good concentration both time frequency constructed real-valued rectangular lattices.