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From a noise performance perspective in communication and control systems, what should be the general guideline regarding the bandwidth of a system?

Difficulty: Easy

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
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