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Digitization Noise in Power Spectral Analysis

L. KristensenRiso National Laboratory, DK-4000 Roskilde, Denmark

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P. KirkegaardRiso National Laboratory, DK-4000 Roskilde, Denmark

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Abstract

It is well-known that the digitization noise variance is Δ2/12 for a continuous time series sampled with the signal resolution Δ. It is also generally accepted that this variance often has a white-power spectral density. We have examined in detail under which circumstances this is the case for turbulent media and found that for a joint Gaussian signal x(t) with variance σ2{x} and a Taylor microscale λ the digitization noise is indeed white if (Δt/λ)(σ{x}/Δ) ≳ t, where Δt is the constant sampling time. Otherwise, the digitization noise tends to be concentrated at lower frequencies. White spectral noise with known variance is easily removed, so from a practical point of view Δt should not be too small.

Abstract

It is well-known that the digitization noise variance is Δ2/12 for a continuous time series sampled with the signal resolution Δ. It is also generally accepted that this variance often has a white-power spectral density. We have examined in detail under which circumstances this is the case for turbulent media and found that for a joint Gaussian signal x(t) with variance σ2{x} and a Taylor microscale λ the digitization noise is indeed white if (Δt/λ)(σ{x}/Δ) ≳ t, where Δt is the constant sampling time. Otherwise, the digitization noise tends to be concentrated at lower frequencies. White spectral noise with known variance is easily removed, so from a practical point of view Δt should not be too small.

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