Using the autocorrelation function to characterize time series of voltage measurements

摘要: The standard deviation of the mean is most common basis for specifying statistical uncertainty repeated measurements, yet it often calculated incorrectly. variance mean, , a time series correlated measurements weakly stationary process correctly expressed in terms autocorrelation function (ACF) at lag k, ρ(k). This approach used to evaluate white voltage noise measured regular intervals τ0 through low pass filter bandwidth B by four methods: (1) developing expression ρ(k) = exp (−4Bτ0k) evaluated estimating from sample spectrum; (2) noting that exp(−4Bτ0) < 1 ACF first-order autoregressive process, AR(1), which readily ; (3) ACF, using cut-off an AR(1) process; and (4) applying general method recently proposed Zhang (2006 Metrologia 43 S276–81), estimate assuming data may be described moving average with deduced themselves. values methods are good agreement. provides firm support Zhang's method; this important because method's wide scope application.