  Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero
function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle
states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this paper is
twofold. First, we present the shift bound for abelian codes with a streamlined
proof. Second, we use the shifting technique to prove a generalization and a
sharpening of the Donoho-Stark uncertainty principle. In particular, the
sharpened uncertainty principle states, with notation above, that
$|\supp(f)||\supp(\hf)|\geq |G|+|\supp(f)|-|H(\supp(f))|$, where $H(\supp(f))$
is the stabilizer of $\supp(f)$ in $G$.
