Topic: Signals and Systems
What is the Nyquist rate for a continuous time signal $x(t)=5~\cos(100\pi t)+2~\sin(200\pi t)$?
- A. 100 Hz
- B. 200 Hz
- C. 400 Hz
- D. 50 Hz
Answer: B. 200 Hz
Explanation: The signal contains two frequency components:
1. $\omega_1 = 100\pi \implies f_1 = 50$ Hz.
2. $\omega_2 = 200\pi \implies f_2 = 100$ Hz.
The maximum frequency component present in the signal is $f_{max} = 100$ Hz.
The Nyquist rate is defined as twice the maximum frequency: $f_s = 2 \times f_{max} = 2 \times 100 = 200$ Hz.