  In the paper we consider the partial sum process
$\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\{X_k^{(n)}=\sum_{j=0}^{\infty}
a_{j}^{(n)}\xi_{k-j}(b(n)), \ k\in \bz\},\ n\ge 1,$ is a series of linear
processes with tapered filter $a_{j}^{(n)}=a_{j}\ind{[0\le j\le \l(n)]}$ and
heavy-tailed tapered innovations $\xi_{j}(b(n), \ j\in \bz$. Both tapering
parameters $b(n)$ and $\l(n)$ grow to $\infty$ as $n\to \infty$. The limit
behavior of the partial sum process (in the sense of convergence of finite
dimensional distributions) depends on the growth of these two tapering
parameters and dependence properties of a linear process with non-tapered
filter $a_i, \ i\ge 0$ and non-tapered innovations. We consider the cases where
$b(n)$ grows relatively slow (soft tapering) and rapidly (hard tapering), and
all three cases of growth of $\l(n)$ (strong, weak, and moderate tapering).
