Question:
The Nyquist sampling rate for a signal band limited to \(4\,kHz\) is
The Nyquist sampling rate for a signal band limited to \(4\,kHz\) is
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Sampling frequency must be ≥ 2 × highest frequency.
Updated On: Jul 2, 2026
- \(5\,kHz\)
- \(8\,kHz\)
- \(2\,kHz\)
- \(16\,kHz\)
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The Correct Option is B
Solution and Explanation
Concept:
Nyquist sampling theorem:
\[
f_s \geq 2f_{max}
\]
Step 1: Given \[ f_{max} = 4\,kHz \]
Step 2: Apply formula \[ f_s = 2 \times 4 = 8\,kHz \]
Step 3: Interpretation Sampling must be at least twice highest frequency.
Step 4: Avoid aliasing Lower sampling leads to distortion.
Step 5: Conclusion \[ \boxed{8\,kHz} \]
Final Answer: \[ \boxed{(B)} \]
Step 1: Given \[ f_{max} = 4\,kHz \]
Step 2: Apply formula \[ f_s = 2 \times 4 = 8\,kHz \]
Step 3: Interpretation Sampling must be at least twice highest frequency.
Step 4: Avoid aliasing Lower sampling leads to distortion.
Step 5: Conclusion \[ \boxed{8\,kHz} \]
Final Answer: \[ \boxed{(B)} \]
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