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Let $a,b,c>0$. We investigate the characterization problem which asks for a classification of all the triples $(a,b,c)$ such that the Weyl-Heisenberg system $\{{\mathrm{e}}^{2\pi \mathrm{i}mbx}{\chi }_{[na,na+c)}:m,n\in \mathbb{Z}\}$ is a frame for $L^2\left(ℝ\right)$. It turns out that the answer to the problem is quite complicated, see Gu and Han (2008) and Janssen (2003). Using a dilation technique, one can reduce the problem to the case where $b=1$ and only let $a$ and $c$ vary. In this paper, we extend the Zak transform technique and use the Fourier analysis technique to study the problem for the case of...