zero-order hold

Practical digital-to-analog converters (DAC) implement an approximation like the zero-order hold.

Discretization of continuous time systems using Zero-order hold (ZOH) and ADCs for digital controller implementation.

The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC).

The zero-order hold is the hypothetical filter or LTI system that converts the sequence of modulated Dirac impulses x(t)to the piecewise-constant signal (shown in Figure 2):

The fact that DACs output a sequence of piecewise constant values (known as zero-order hold in sample data textbooks) or rectangular pulses causes multiple harmonics above the Nyquist frequency.