  Let $G $ be a noncompact semisimple Lie group with finite centre. Let $X=G/K$
be the associated Riemannian symmetric space and assume that $X$ is of rank
one. The spectral projections associated to the Laplace-Beltrami operator are
given by $P_{\lambda}f =f\ast \Phi_{\lambda}$, where $\Phi_{\lambda}$ are the
elementary spherical functions on $X$. In this paper, we prove an Ingham type
uncertainty principle for $P_{\lambda}f$. Moreover, similar results are
obtained in the case of spectral projections associated to Dunkl Laplacian.
