Sampling and quantization

If a digital system is embedded in the physical world, input signals must be sampled and quantized as follows:

An anti-aliasing filter and sampler is followed by an analog-to-digital (A/D) converter. Its function is to convert each sample (mathematically a real number) into a finite set of values. The sampler makes the signal discrete in time, and the A/D converter makes it discrete in amplitude.
After a signal is processed digitally, it can be converted back to continuous amplitude and time as follows:

The analog-to-digital (D/A) converter creates a continuous-time signal that looks like the following:

The D/A converter holds, for one sample period, a value equal to the sample. This continuous-time signal has high frequency components that are artifacts of the "square-wave" approximation to the signal. We know that the continuous-time signal has frequency components no higher than half the sampling rate. The reconstruction filter is a LPF that eliminates the unwanted frequency components.

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