The accuracy of zero order hold (ZOH) depends on the sampling frequency. When T → 0, the output of ZOH approaches the continuous time signal. Zero order hold is again a linear device which satisfies the principle of superposition.

Figure 2: Impulse response of ZOH

The impulse response of a ZOH, as shown in Figure 2, can be written as

Since $T = \dfrac{2\pi}{w_{s}}$ , we can write

$\displaystyle G_{ho}(jw)$ = $\displaystyle \frac{2\pi}{w_{s}}\frac{\sin(\pi w/w_{s})}{\pi w/w_{s}}\ e^{-j\pi w/w_{s}}$