Signal averaging and noise calculator
Averaging n independent samples cuts random noise by the square root of n. It never removes systematic error.
Hz
Noise after averaging
0.625
- Noise improvement
- 18.062 dB
- Effective extra bits of resolution
- 3.000
- Signal to noise ratio after
- 44.082 dB
- Signal to noise ratio before
- 26.021 dB
- Time to gather the samples
- 0.064 00 s
- Effective update rate
- 15.625 Hz
- Total error including the offset
- 2.095 38
- Samples beyond which the offset dominates
- 6
Show the working
- Noise on one sample = 5
- Samples averaged = 64
- Sample rate = 1000
- Signal amplitude = 100
- Systematic offset = 2
- Noise after averaging = 5 / sqrt(64) = 0.625
- Noise improvement = 10 * log10(64) = 18.0618
- Effective extra bits of resolution = log2(64) / 2 = 3
- Signal to noise ratio before = 20 * log10(100/5) = 26.0206
- Signal to noise ratio after = 20 * log10(100/0.625) = 44.0824
- Time to gather the samples = 1000 > 0 ? 64/1000 : 0 = 0.064
- Effective update rate = 0.064 > 0 ? 1/0.064 : 0 = 15.625
- Total error including the offset = hypot(0.625, 2) = 2.095 38
- Samples beyond which the offset dominates = 2 > 0 ? (5/2)^2 : 0 = 6.25
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- averaged noise = noise / sqrt(n)
- each factor of four in samples buys one extra bit of effective resolution
Averaging past the point where systematic error dominates is wasted time. The last row shows where that is.
Averaging only works on independent noise. Mains hum is correlated, and needs a notch filter or synchronous sampling instead.