Topic: Signals and Systems
A continuous time signal has frequency content at f = 10 MHz, 50 MHz and 70 MHz. The signal is sampled at sampling frequency of 56 MHz. The frequency content of output will be
- A. 10 MHz
- B. 10 MHz and 6 MHz
- C. 10 MHz, 6 MHz and 14 MHz
- D. 46 MHz
Answer: C. 10 MHz, 6 MHz and 14 MHz
Explanation: When a signal is sampled at $f_s$, the aliased frequencies fold down into the baseband according to $|f_{in} - kf_s|$. For $f_1 = 10$ MHz, the frequency is natively 10 MHz. For $f_2 = 50$ MHz, the baseband alias is $|56 - 50| = 6$ MHz. For $f_3 = 70$ MHz, the baseband alias is $|56 - 70| = 14$ MHz. Thus, the output frequency content will be 10 MHz, 6 MHz, and 14 MHz.