Definition

The zero-order hold (ZOH) method is a technique used in digital signal processing to reconstruct a continuous-time signal from a discrete-time one.

Methodology

Sampling - The continuous-time signal is sampled at regular intervals (the sampling period).

Holding - The value of each sample is held constant until the next sample arrives. This creates a piecewise-constant signal that resembles a staircase.

Mathematical Representation

If you have a discrete-time signal $x[n]$ :

where:

• $T$ is the sampling period
• $n$ is the sample index

Applications

Digital-to-Analog Conversion (DAC) - ZOH is commonly used in DACs to convert digital signals into analog signals that can drive real-world systems.

Control Systems - ZOH is used in control systems to model the behavior of systems that receive digital control inputs but operate in continuous time.

Key Points

The zero-order hold is a simple and practical way to reconstruct signals.

It introduces a delay of one-half the sample period into the reconstructed signal.

The reconstructed signal contains higher-order harmonics due to the sharp steps, which might need filtering in some applications.