Exercise · ZW-ALIASING-009 · ★★☆ Intermediate
Two sinusoids of \(2\,\text{Hz}\) and \(8\,\text{Hz}\) are sampled at \(f_s = 10\,\text{Hz}\). Which statement is correct?
Choose one option.
Show answer
- A. Both produce the same samples
Explanation
The 8 Hz one folds to \(|8-10| = 2\,\text{Hz}\), so both give the same samples. Thinking that being below \(f_s\) is enough is a common mistake.
Review the concept: Aliasing
Aliasing is the overlap of spectral replicas that occurs when a signal is sampled at a rate below twice its bandwidth, so that different frequencies become indistinguishable from one another.
\[f_{\text{alias}} = |f - k\,f_s|, \quad k \in \mathbb{Z}\]
More practice problems: aliasing
- ZW-ALIASING-001 What condition avoids aliasing when sampling a signal with maximum frequency f_max?
- ZW-ALIASING-002 What is the Nyquist frequency for sampling at f_s = 200 Hz?
- ZW-ALIASING-003 A signal has a maximum frequency of 30 Hz. What is the minimum sampling frequency that avoids alias…
- ZW-ALIASING-004 What phenomenon does the apparent frequency obtained after sampling below the Nyquist rate describe?
- ZW-ALIASING-005 What type of filter is used before sampling to limit the bandwidth and avoid aliasing?
- ZW-ALIASING-006 A 8 Hz sinusoid is sampled at f_s = 10 Hz. What is the apparent frequency after sampling?
- ZW-ALIASING-007 A signal with components up to 40 Hz is sampled at f_s = 60 Hz. Does aliasing occur?
- ZW-ALIASING-008 A signal contains cos (2π · 3t) and is sampled at f_s = 4 Hz. What apparent frequency is observed?