Mathematical Analysis of Average Response Values for Nonstationary Data

Quantitative results are derived for the accuracy to be associated with average response computations on a wide class of nonstationary physical data as a function of underlying signal and noise properties and the sample size used by the average response computer. Input and output SNR's are defined in terms of these quantities. Statistical confidence bands are determined for both arbitrary probability distributions and for Gaussian probability distributions, which indicate how closely a measured sample mean value approximates the true mean value at any time.