This paper studies the cardinal interpolation operators associated with the general multiquadrics, *ϕ*_{α, c}(*x*)=(∥*x*∥^{2} + *c*^{2})^{α},
$x\in \mathbb {R}^{d}$
. These operators take the form
$$\mathcal{I}_{\alpha,c}\mathbf{y}(x) = \sum\limits_{j\in\mathbb{Z}^{d}}y_{j}L_{\alpha,c}(x-j),\quad\mathbf{y}=(y_{j})_{j\in\mathbb{Z}^{d}},\quad x\in\mathbb{R}^{d}, $$
where *L*_{α, c} is a fundamental function formed by integer translates of *ϕ*_{α, c} which satisfies the interpolatory condition
$L_{\alpha ,c}(k) = \delta _{0,k},\; k\in \mathbb {Z}^{d}$
. We consider recovery results for interpolation of bandlimited functions in higher dimensions by limiting the parameter
$c\to \infty $
. In the univariate case, we consider the norm of the operator
$\mathcal {I}_{\alpha ,c}$
acting on *ℓ*_{p} spaces as well as prove decay rates for *L*_{α, c} using a detailed analysis of the derivatives of its Fourier transform,
$\widehat {L_{\alpha ,c}}$
.