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:

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.

Discretize the model again

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