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Check: signal bandwidth and noise bandwidth
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An ideal one-pole low-pass has fc = 100 Hz. Its input noise is white over the relevant frequencies, and no additional filtering is present. Distinguish the signal −3 dB corner from the integral that determines output mean-square noise.
Which noise bandwidth should multiply white-noise power density?
The one-pole white-noise equivalent bandwidth is (π/2)fc = 157.079633 Hz. Using fc directly underestimates integrated white-noise power. This result assumes the ideal one-pole response extends over the noise spectrum.
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