Quantization maps a sample value to a finite set of permissible values by rounding to the nearest; the maximum quantization error equals S/2, where S is the step size.

Quantization maps a sample value to a finite set of permissible values by rounding to the nearest; the maximum quantization error equals S/2, where S is the step size.

• A. S/2
• B. S
• C. S/4
• D. 0

Answer: (A)

When a uniform quantizer rounds a sample to the nearest level, the levels are spaced by S. The error is the distance from the original value to the chosen level. Since you always pick the nearest level, this distance cannot exceed half the distance between adjacent levels, which is S/2. The worst-case happens when the value lies exactly midway between two levels, giving an error of S/2. Therefore, the maximum quantization error is S/2.

When a uniform quantizer rounds a sample to the nearest level, the levels are spaced by S. The error is the distance from the original value to the chosen level. Since you always pick the nearest level, this distance cannot exceed half the distance between adjacent levels, which is S/2. The worst-case happens when the value lies exactly midway between two levels, giving an error of S/2. Therefore, the maximum quantization error is S/2.