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A longstanding problem in Gabor theory is to identify time-frequency shifting lattices a\mathbb{Z}\times b\mathbb{Z} and ideal window functions \chi_I on intervals I of length c such that \{e^{-2\pi i n bt} \chi_I(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\} are Gabor frame…