Question

Calculate the Nyquist rate for a signal with a maximum frequency component of 5 kHz.

• A. 5 kHz
• B. 10 kHz
• C. 2.5 kHz
• D. 20 kHz

Hint:

Nyquist Rate = 2 × Maximum frequency → Prevents aliasing.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Nyquist Sampling Theorem states that to accurately reconstruct a signal from its samples without aliasing, the sampling frequency must be at least twice the maximum frequency component of the signal.
Step 2: Key Formula or Approach:
The Nyquist rate is defined as:
\[ f_s = 2 \times f_{\text{max}} \]
Step 3: Detailed Explanation:
Given the maximum frequency component ($f_{\text{max}}$) = $5$ kHz.
Applying the formula:
\[ \text{Nyquist Rate} = 2 \times 5\text{ kHz} = 10\text{ kHz} \]
Sampling at exactly $10$ kHz is the minimum requirement; sampling at any rate lower than this will cause spectral overlapping (aliasing).
Step 4: Final Answer:
The Nyquist rate for the $5$ kHz signal is $10$ kHz.