  Understanding dissipative and decohering processes is fundamental to the
study of quantum systems. An accurate and generic method for investigating
these processes is to simulate both the system and environment, which, however,
is computationally very demanding. We develop a novel approach to constructing
finite representations of the environment based on the influence of different
frequency scales on the system's dynamics. As an illustration, we analyze a
solvable model of an optical mode decaying into a reservoir. The influence of
the environment modes is constant for small frequencies, but drops off rapidly
for large frequencies, allowing for a very sparse representation at high
frequencies that gives a significant computational speedup in simulating the
environment. This approach provides a general framework for simulating open
quantum systems.
