An engineer needs to digitize an ECG signal with frequency components up to 500 Hz and must resolve voltage differences as small as 10 μV. Which ADC specification combination is most appropriate?
Af_s = 500 Hz, N = 8 bits — matches the signal frequency and provides adequate precision
Bf_s = 2000 Hz, N = 16 bits — satisfies Nyquist and provides high voltage resolution
Cf_s = 2000 Hz, N = 8 bits — satisfies Nyquist; bit depth is irrelevant for medical signals
Df_s = 500 Hz, N = 16 bits — high bit depth compensates for a low sampling rate
The Nyquist criterion requires f_s > 2·f_max = 2·500 Hz = 1000 Hz, so f_s = 2000 Hz provides adequate margin. Resolving 10 μV requires many quantization levels — a 16-bit ADC with a 3.3V reference has an LSB of about 50 μV, which is marginal but far better than 8 bits (LSB ≈ 12.9 mV). These are independent dimensions: sampling rate prevents aliasing (temporal), while bit depth sets voltage precision. Option D illustrates the classic misconception — a low sampling rate will alias high-frequency components regardless of bit depth.
Question 2 Multiple Choice
After digitizing an audio recording, a strange tone appears in the output that was not present in the original signal. What is the most likely cause?
AThe DAC used too few bits when playing back the signal, introducing quantization noise
BThe sampling rate was below twice the highest signal frequency, causing high-frequency components to alias into the signal band
CThe sample-and-hold circuit was too slow, causing adjacent samples to blur together
DThe R-2R ladder resistors were mismatched, producing nonlinearity in the DAC output
Aliasing is the only mechanism that creates spurious tones that were not in the original signal. When f_s < 2·f_max, high-frequency components 'fold back' into the signal band and appear as false low-frequency tones. Crucially, these alias tones are indistinguishable from real signal content once digitized — they cannot be removed by post-processing. The fix must happen before sampling: an analog anti-aliasing filter that attenuates all frequencies above f_s/2. The other options affect signal quality (noise floor, linearity) but do not create phantom tones.
Question 3 True / False
Increasing an ADC's sampling rate from 44.1 kHz to 192 kHz will allow it to resolve smaller voltage differences between samples.
TTrue
FFalse
Answer: False
Sampling rate and voltage resolution are completely independent. Sampling rate determines how fast the signal can change (temporal resolution) and what maximum signal frequency can be captured without aliasing. Voltage resolution — the smallest detectable voltage step — is determined entirely by bit depth (N): LSB = V_ref / 2^N. A 16-bit ADC at 44.1 kHz has the same voltage precision as a 16-bit ADC at 192 kHz. To resolve smaller voltages, you need more bits, not a higher sampling rate.
Question 4 True / False
Once aliasing has occurred during analog-to-digital conversion, the original signal cannot be fully recovered by digital filtering alone.
TTrue
FFalse
Answer: True
This is a fundamental and irreversible consequence of violating the Nyquist criterion. When frequencies above f_s/2 are sampled, they fold back into the 0 to f_s/2 band and appear at exactly the same frequencies as legitimate low-frequency signal content. There is no way to distinguish the aliased components from real signal components after the fact — the information needed to separate them is destroyed. This is why an analog anti-aliasing low-pass filter, applied before the ADC, is mandatory in any real system. Digital filtering after the fact can only remove known frequencies, not separate aliased components from legitimate ones at the same frequency.
Question 5 Short Answer
A student argues that buying a higher-sample-rate ADC always gives a better recording because 'more samples mean more information.' Identify the flaw in this reasoning and explain what capturing 'more information' actually requires.
Think about your answer, then reveal below.
Model answer: The flaw is conflating two independent dimensions of ADC performance. A higher sampling rate captures faster-changing signals and prevents aliasing of higher frequencies — it adds temporal resolution. But 'more information' about amplitude (voltage) requires more bits, not more samples. A 1 MHz sampling rate with 8-bit resolution still rounds every sample to one of only 256 voltage levels. Capturing more precise voltage information requires increasing bit depth (N), which doubles the number of quantization levels and improves the SQNR by approximately 6 dB per additional bit. Truly better recordings require both adequate sampling rate (to avoid aliasing) AND sufficient bit depth (for voltage precision).
This misconception is extremely common. The two parameters are orthogonal: sampling rate governs the time axis (how fast the signal can vary), while bit depth governs the amplitude axis (how precisely each sample is measured). Professional audio uses 96 kHz / 24-bit not because one compensates for the other, but because the temporal and amplitude requirements must each be satisfied independently.