Converting continuous-time transfer functions such as
and
to the digital domain is analogous to converting an analog
electrical filter to a corresponding digital filter--a problem which
has been well studied [346]. For this task, the
bilinear transform (§7.3.2) is a good choice. In
addition to preserving order and being free of aliasing, the bilinear
transform preserves the positive-real property of passive impedances
(§C.11.2).
Digitizing
via the bilinear transform (§7.3.2)
transform gives
which is a second-order digital filter having gain less than one at all frequencies--i.e., it is a Schur filter that becomes an allpass as the damping