Exercise · ZW-ALIASING-008 · ★★☆ Intermediate
A signal contains \(\cos(2\pi \cdot 3t)\) and is sampled at \(f_s = 4\,\text{Hz}\). What apparent frequency is observed?
Choose one option.
Show answer
- B. \(1\,\text{Hz}\)
Explanation
Since \(3 > 2\), the apparent frequency is \(|3 - 4| = 1\,\text{Hz}\). Returning the original frequency without folding it is a common error.
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-009 Two sinusoids of 2 Hz and 8 Hz are sampled at f_s = 10 Hz. Which statement is correct?