On a complementary condition to derivation of discrete Gabor expansions

In a recent letter, a complementary condition to the condition in Wexler and Raz (1990) for the discrete Gabor expansion (DGE) was derived and, consequently, the resulting DGE may admit rational oversampling rates. In the present letter, we first modify the condition in Li and Qian (1995), and then demonstrate a new relaxed complementary condition for the DGE in which the range of the time and frequency parameters is increased. Moreover, we will show that the new condition with the increased parameter range is equivalent to the condition in Wexler and Raz but with different parameters.