Pre-filtering to avoid aliasing
we need anti-aliasing filter because there is no Band limited signal in real world. In real world, there are no delta function and continuous function (original target signal)

1. Anti-aliasing filter
prefiltering

2. Sampling filter
sample and hold
ideal case is Sinc interpolation.
3. A/D filter
quantization (quantization error occurs)
4. DT system
5. D/A filter
The digitalization hold continuous function (ZOH like) and zoh is rectangular convolution (quantization error)

6. Compensation filter
Because multiplied sinc not rectangualar in frequency domain, we compensate by another function to compensate quantization error

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.
https://en.wikipedia.org/wiki/Zero-order_hold

Seonglae Cho