Book Description

This analysis investigates fundamental statistical questions concerned with measuring the power spectrum (i.e., power spectral density func ion) and the cross-power spectrum associated with random phenomena. The analysis treats in detail a practical engineering (analog) technique for making such measurements which employs a filter and multiplier. Quantitative formulas are derived for predicting the ean square error to be expect d in a set of estimates as a function of the length of t e record, the bandwidth of the filter, and the true nature of the spectrum. Discrete (digital) pproximations to the continuous (analog) formulas are developed base on sampling the data at equispaced intervals. Confidence limits and experimental design relations are included in the analysis. An explanation is given from a broad viewpoint on basic ideas of probability theory, random processes, and general matters of statistical estim tion. The analysis examines briefly how to determine the mean value and the correlation functions for a pair of random processes. (Author).