Topic: Communication Systems
An FM signal at 10.7 MHz IF needs to be digitized for demodulation in a digital domain. If the bandwidth of this signal is 200 kHz, the maximum usable sampling frequency is
- A. 200 kHz
- B. 600 kHz
- C. 400 kHz
- D. 800 kHz
Answer: C. 400 kHz
Explanation: Center frequency $f_{c}=10.7~\text{MHz}$, Bandwidth $BW=200~\text{kHz} = 0.2~\text{MHz}$.
Upper frequency $f_{H} = f_{c} + \frac{BW}{2} = 10.7 + 0.1 = 10.8~\text{MHz}$.
The maximum usable sampling frequency $f_{s}$ for bandpass sampling is given by $f_{s}=\frac{2f_{H}}{k}$, where $k = \lfloor \frac{f_{H}}{BW} \rfloor$.
$k = \lfloor \frac{10.8}{0.2} \rfloor = \lfloor 54 \rfloor = 54$.
$f_{s}=\frac{2 \times 10.8~\text{MHz}}{54} = \frac{21.6~\text{MHz}}{54} = 0.4~\text{MHz} = 400~\text{kHz}$.