Suppose $g\in L^{2}(\mathbb{R})$ and $g_{{m,n}}(x)=e^{{2\pi imx}}g(x-n)$, where $m,n\in\mathbb{Z}$. If $\{g_{{m,n}}:m,n\in\mathbb{Z}\}$ is an orthonormal basis for $L^{2}(\mathbb{R})$, then either