In an ADC, what is the difference between resolution and sampling rate, and how is quantization error determined?

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Multiple Choice

In an ADC, what is the difference between resolution and sampling rate, and how is quantization error determined?

Explanation:
The key idea is that resolution and sampling rate describe two different aspects of an ADC: resolution tells you how finely the amplitude is quantized, while sampling rate tells you how often you take samples in time. Resolution is the number of bits per sample, so more bits give more quantization levels. The step size between those levels is Δ = full-scale range / 2^N, where N is the number of bits. The quantization error is the difference between the true analog value and the quantized level, and for a uniform quantizer this error is bounded and typically modeled as within ±Δ/2 (often treated as a uniform random error between -Δ/2 and +Δ/2). Therefore, the correct description is that resolution is the number of bits per sample, sampling rate is samples per second, and the quantization error is approximately ±Δ/2 with Δ defined as the full-scale range divided by 2^N.

The key idea is that resolution and sampling rate describe two different aspects of an ADC: resolution tells you how finely the amplitude is quantized, while sampling rate tells you how often you take samples in time. Resolution is the number of bits per sample, so more bits give more quantization levels. The step size between those levels is Δ = full-scale range / 2^N, where N is the number of bits. The quantization error is the difference between the true analog value and the quantized level, and for a uniform quantizer this error is bounded and typically modeled as within ±Δ/2 (often treated as a uniform random error between -Δ/2 and +Δ/2). Therefore, the correct description is that resolution is the number of bits per sample, sampling rate is samples per second, and the quantization error is approximately ±Δ/2 with Δ defined as the full-scale range divided by 2^N.

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