Quantization: Discretizing the Amplitude Axis

The Second Half of Digitization

After sampling discretizes the time axis, quantization discretizes the amplitude axis. A sampled signal $x[n]$ still takes continuous amplitude values—infinite precision that digital systems cannot represent. Quantization maps these to a finite set of levels.

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What Is Quantization?

Quantization is the process of mapping a continuous (or high-resolution) range of amplitude values to a finite set of discrete levels.

A quantizer with $L$ levels divides the input range $[-V_{\text{max}}, V_{\text{max}}]$ into $L$ intervals, each of width $\Delta$ (step size):

\[\Delta = \frac{2V_{\text{max}}}{L} = \frac{\text{Full-Scale Range}}{L}\]

Each input value $x$ is mapped to the nearest quantization level (midpoint of its interval).

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