  The employ of a noiseless linear amplifier (NLA) has been proven as a useful
tool for mitigating imperfections in quantum channels. Its analysis is usually
conducted within specific frameworks, for which the set of input states for a
given protocol is fixed. Here we obtain a more general description by showing
that a noisy and lossy Gaussian channel followed by a NLA has a general
description in terms of effective channels. This has the advantage of offering
a simpler mathematical description, best suitable for mixed states, both
Gaussian and non-Gaussian. We investigate the main properties of this effective
system, and illustrate its potential by applying it to loss compensation and
reduction of phase uncertainty.
