Zero-order hold

The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication.

A zero-order hold reconstructs the following continuous-time waveform from a sample sequence x[n], assuming one sample per time interval T:

The function ${\displaystyle \mathrm {rect} \left({\frac {t-T/2}{T}}\right)}$ is depicted in Figure 1, and ${\displaystyle x_{\mathrm {ZOH} }(t)\,}$ is the piecewise-constant signal depicted in Figure 2.

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