Creating and Manipulating Models | ![]() ![]() |
Zero-Order Hold
Zero-order hold (ZOH) devices convert sampled signals to continuous-time signals for analyzing sampled continuous-time systems. The zero-order-hold discretization of a continuous-time LTI model
is depicted in the following block diagram.
The ZOH device generates a continuous input signal u(t) by holding each sample value u[k] constant over one sample period.
The signal is then fed to the continuous system
, and the resulting output
is sampled every
seconds to produce
.
Conversely, given a discrete system , the
d2c
conversion produces a continuous system whose ZOH discretization coincides with
. This inverse operation has the following limitations:
d2c
cannot operate on LTI models with poles at d2c
conversion of a discrete system with negative real poles produces a continuous system with higher order.
The next example illustrates the behavior of d2c
with real negative poles. Consider the following discrete-time ZPK model.
Use d2c
to convert this model to continuous-time
and you get a second-order model.
and you get back the original discrete-time system (up to canceling the pole/zero pair at z=-0.5):
![]() | Continuous/Discrete Conversions of LTI Models | First-Order Hold | ![]() |