From a noise performance perspective in communication and control systems, what should be the general guideline regarding the bandwidth of a system?
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AIt should be very large
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BIt should not be too large
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CIt should be as large as possible under all conditions
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DIt should be infinite
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EIt should always be very small regardless of application
Answer
Correct Answer: It should not be too large
Explanation
Introduction / Context:Noise in electronic systems is distributed over frequency. Thermal noise, for instance, is white across a broad spectrum, meaning total noise power is directly proportional to bandwidth. Therefore, system bandwidth must be carefully chosen to balance fidelity and noise performance.
Given Data / Assumptions:
- Noise power spectral density ≈ constant across wideband (white noise assumption).
- Total integrated noise power = N0 × bandwidth.
- Signal occupies a certain frequency range.
Concept / Approach:To minimize noise, bandwidth should not greatly exceed the minimum required to pass the signal. Too large a bandwidth admits unnecessary noise power, degrading signal-to-noise ratio (SNR). Conversely, too narrow a bandwidth distorts or attenuates the signal. Optimal design uses bandwidth just sufficient to accommodate the signal spectrum with margin.
Step-by-Step Solution:
Signal requires bandwidth B_sig.Noise power = N0 × B_total.If B_total ≫ B_sig, then excess noise enters without improving fidelity.Best choice: B_total slightly larger than B_sig to ensure fidelity but limit noise.Verification / Alternative check:
Shannon's capacity theorem C = B log2(1 + S/N) also implies that while capacity increases with B, the S/N decreases as noise power increases linearly with B.Why Other Options Are Wrong:
'Very large', 'as large as possible', or 'infinite' bandwidth increases noise and is undesirable.'Always very small' sacrifices signal fidelity and data rate.Common Pitfalls:
Thinking maximum bandwidth is always best; overlooking the tradeoff between SNR and fidelity.Final Answer:
It should not be too large