Uncertainty principles for generating systems $\{e_n\}_{n=1}^{\infty} \subset
\ltwo$ are proven and quantify the interplay between $\ell^r(\N)$ coefficient
stability properties and time-frequency localization with respect to $|t|^p$
power weight dispersions. As a sample result, it is proven that if the
unit-norm system $\{e_n\}_{n=1}^{\infty}$ is a Schauder basis or frame for
$\ltwo$ then the two dispersion sequences $\Delta(e_n)$, $\Delta(\bar{e_n})$
and the one mean sequence $\mu(e_n)$ cannot all be bounded. On the other hand,
it is constructively proven that there exists a unit-norm exact system
$\{f_n\}_{n=1}^{\infty}$ in $\ltwo$ for which all four of the sequences
$\Delta(f_n)$, $\Delta(\bar{f_n})$, $\mu(f_n)$, $\mu(\bar{f_n})$ are bounded.