  When chaotic signals are used in practical communication systems, it is
essential to control and eventually limit the spectral bandwidth occupied by
these signals. One way to achieve this goal is to insert a discrete-time filter
into a nonlinear map that generates chaotic signals. However, this can
completely change the dynamic properties of the original map. Considering this
situation, this paper presents a series of numerical experiments aimed at
obtaining the Lyapunov exponents of the signals generated by the
two-dimensional H\'enon map with a set of prototypical finite impulse response
(FIR) filters added in the feedback loop. Our results show that the number of
filter coefficients and the location of the zeros have a significant and
complex impact on the behavior of the generated signals. Therefore, FIR filters
should be carefully designed to preserve or suppress chaos in practical
applications.
