  An extension of sinc interpolation on $\mathbb{R}$ to the class of
algebraically decaying functions is developed in the paper. Similarly to the
classical sinc interpolation we establish two types of error estimates. First
covers a wider class of functions with the algebraic order of decay on
$\mathbb{R}$. The second type of error estimates governs the case when the
order of function's decay can be estimated everywhere in the horizontal strip
of complex plane around $\mathbb{R}$. The numerical examples are provided.
