Topic: Communication Systems
Consider the sampling of the band-pass signal, whose spectrum is as shown below. What minimum sampling frequency would you use from the options given below, so as to avoid aliasing?
(The spectrum is a triangle from 94 Hz to 106 Hz with peak at 100 Hz).
- A. 24 Hz
- B. 26.5 Hz
- C. 48 Hz
- D. 212 Hz
Answer: B. 26.5 Hz
Explanation: $F_H = 106~\text{Hz}$, $F_L = 94~\text{Hz}$.
Bandwidth $BW = F_H - F_L = 106 - 94 = 12~\text{Hz}$.
$K = \lfloor \frac{F_H}{BW} \rfloor = \lfloor \frac{106}{12} \rfloor = 8$.
Minimum sampling frequency $F_s = \frac{2F_H}{K} = \frac{2(106)}{8} = \frac{212}{8} = 26.5~\text{Hz}$.