Topic: Communication Systems
A signal $1+\cos(2\pi ft)+\cos(6\pi ft)$ where $f=1\text{ MHz}$ is sampled at 3 MHz and Fourier Transform is carried out. How many lines will be seen in Fourier Transform?
- A. 5
- B. 1
- C. 3
- D. 2
Answer: C. 3
Explanation: The signal has frequency components at DC ($0\text{ MHz}$), $f = 1\text{ MHz}$, and $3f = 3\text{ MHz}$. When sampled at $3\text{ MHz}$, the $3\text{ MHz}$ component aliases to $0\text{ MHz}$ (DC). The $1\text{ MHz}$ component remains at $1\text{ MHz}$. Thus, in the baseband spectrum, there will be spectral lines at $-1\text{ MHz}$, $0\text{ Hz}$, and $+1\text{ MHz}$, totaling 3 spectral lines.