Question E4A06:
What is the effect of aliasing on a digital oscilloscope when displaying a waveform?  

Choices:  
A: A false, jittery low-frequency version of the waveform is displayed  
B: The waveform DC offset will be inaccurate  
C: Calibration of the vertical scale is no longer valid  
D: Excessive blanking occurs, which prevents display of the waveform    

Correct Answer is  A: A false, jittery low-frequency version of the waveform is displayed  

To display a waveform correctly, a digital oscilloscope must sample fast enough. If it doesn’t, aliasing occurs.

Why A is correct:
- Aliasing happens when the sampling rate $f_s$ is too low to capture the true frequency content of the signal. Per the Nyquist criterion:
  $$f_s \ge 2\,f_{\max}$$
- If a sine wave at $f_{in}$ exceeds $f_s/2$, the scope shows a false, lower-frequency “alias”:
  $$f_{alias} = \big|\,f_{in} - n f_s\,\big| \quad \text{(choose integer $n$ so } f_{alias} \le \tfrac{f_s}{2}\text{)}$$
- This aliased display often looks like a slow, jittery waveform because the apparent frequency is the beat between $f_{in}$ and the sampling clock. Hence: “a false, jittery low-frequency version” of the waveform.

Why the other choices are incorrect:
- B: “The waveform DC offset will be inaccurate” — Aliasing relates to time sampling of higher frequencies, not DC. A DC component (0 Hz) is below Nyquist and is not mispositioned by aliasing.
- C: “Calibration of the vertical scale is no longer valid” — Vertical (amplitude) calibration is unaffected by aliasing. Aliasing is a time/frequency sampling artifact, not a gain calibration issue.
- D: “Excessive blanking occurs” — Blanking is a CRT-era display issue, not the symptom of aliasing in digital scopes.

Useful formulas and rules of thumb:
- Nyquist-Shannon sampling condition:
  $$f_s \ge 2\,f_{\max}$$
- Aliased frequency for a pure tone:
  $$f_{alias} = \big|\,f_{in} - \text{round}\!\left(\frac{f_{in}}{f_s}\right) f_s\,\big|$$
- Practical rule: For clean displays and edges, aim for $f_s \ge 5$ to $10 \times f_{\max}$, and use the scope’s analog bandwidth limit or anti-alias filter when available.
- Example: If $f_s = 12$ MSa/s and $f_{in} = 10$ MHz:
  $$f_{alias} = |10 - 1\cdot 12| = 2\ \text{MHz}$$
  The scope may show a “2 MHz” signal that jitters—classic aliasing.