Question E4A01:
Which of the following limits the highest frequency signal that can be accurately displayed on a digital oscilloscope?  

Choices:  
A: Sampling rate of the analog-to-digital converter  
B: Analog-to-digital converter reference frequency  
C: Q of the circuit  
D: All these choices are correct    

Correct Answer is  A: Sampling rate of the analog-to-digital converter  

To accurately display the highest frequency on a digital oscilloscope, you must sample fast enough to avoid aliasing.

Why A is correct (Sampling rate of the ADC):
- The Nyquist-Shannon theorem says you must sample at least twice the highest frequency component to reconstruct or accurately display it.
- If the sampling rate is $f_s$, then the highest input frequency that can be accurately displayed is bounded by the Nyquist frequency:
  $$f_{max} \le \frac{f_s}{2}$$
- If $f_{in} > \frac{f_s}{2}$, aliasing occurs and the scope shows a false lower frequency:
  $$f_{alias} = \left| f_{in} - n f_s \right| \quad \text{for some integer } n$$

Why the other choices are incorrect:
- B: ADC reference frequency — The ADC’s reference is about amplitude scaling or a stable timebase reference, not the upper input frequency limit. The sampling rate, not a “reference frequency,” sets the Nyquist limit.
- C: Q of the circuit — The quality factor pertains to resonant circuits, not the oscilloscope’s sampling requirement. It doesn’t determine the scope’s max displayable frequency.
- D: All these choices are correct — False because only the sampling rate sets the Nyquist limit in this context.

Useful rules of thumb:
- Minimum to avoid aliasing: $$f_s \ge 2 \, f_{signal}$$
- For a cleaner waveform display (more points per cycle): $$f_s \approx 2.5\text{–}5 \times f_{signal}$$
- For pulses/edges, even higher oversampling (and adequate analog bandwidth) is desirable.

Note: In practice, the oscilloscope’s analog front-end bandwidth must also exceed the signal frequency, but the fundamental limit for accurate digital display is set by the sampling rate.