Sampling and quantization fundamentals: evaluate the statement—“The change in value of the analog signal during the sampling process produces what is called the quantization error.”

Introduction / Context:
In analog-to-digital conversion, several distinct error mechanisms exist. Two commonly confused terms are “quantization error” and “aperture (sampling) error.” This question probes whether changes in the analog signal during sampling are the cause of quantization error.

Given Data / Assumptions:

• Ideal N-bit ADC with a defined quantization step size q.
• A sample-and-hold (S/H) stage that acquires a sample during a finite aperture time.
• A possibly time-varying input at the moment of sampling.

Concept / Approach:
Quantization error results from rounding the held analog value to the nearest discrete digital code. It is bounded by ±q/2 for an ideal mid-tread converter and exists even if the input is perfectly constant during sampling. In contrast, changes in the signal during the acquisition (finite aperture time or jitter of the sampling instant) cause aperture error or sampling uncertainty, not quantization error. Therefore, attributing quantization error to signal change during sampling is incorrect.

Step-by-Step Solution:

Verification / Alternative check:
Set input to a stable DC reference; quantization error remains. Conversely, if the input slews rapidly and the aperture is finite, additional error appears even with infinite resolution—evidence that this extra component is not quantization.

Why Other Options Are Wrong:
“Correct” and conditional variants misidentify the mechanism; flash ADCs and large hold capacitors affect bandwidth/acquisition but do not redefine quantization error.

Common Pitfalls:
Using “quantization” as a catch-all for ADC errors; ignoring aperture jitter; assuming larger capacitors eliminate quantization (they do not).

Final Answer:
Incorrect