While the digital mass simulator has the desirable properties of the bilinear transform,
it is also not perfect from a practical point of view:
(1) There is a pole at half the sampling rate (
).
(2) There is a delay-free path from input to output.
The first problem can easily be circumvented by introducing a loss factor
,
moving the pole from
to
, where
and
. This
is sometimes called the ``leaky integrator''.
The second problem arises when making loops of elements (e.g., a mass-spring chain which forms a loop). Since the individual elements have no delay from input to output, a loop of elements is not computable using standard signal processing methods. The solution proposed by Alfred Fettweis is known as ``wave digital filters,'' a topic taken up in §F.1.