The use of standard techniques for measuring the power spectra of stationary phenomena in the treatment of nonstationary physical phenomena can lead to erroneous results. Some of the tools available for the analysis of nonstationary random phenomena are outlined in this report and the applicability of these tools to some practical engineering problems is discussed.
In scientific research it is frequently desirable to make an accurate measurement of the power spectrum of a complicated time-varying signal. The performance of a Sona-Graph Audio Spectrum Analyzer can be upgraded for this purpose by changing the output format from a carbon-deposited paper that is burned by an electric arc to an oscilloscope and camera system. The time resolution is improved, and direct amplitude measurements are now possible. The utility of the system is demonstrated by analysis of samples of VLF and ULF emissions. The technique can be used in many fields of scientific research, such as geophysics, oceanography, biology, medicine, and acoustics. (Author).
An unabridged and corrected republication of Part I and Part II of The measurement of power spectra from the point of view of communications engineering, which originally appeared in the January 1958 and March 1958 issues of volume XXXVII of the Bell system technical journal.
The use of spectral techniques for the computation of the expected power output of linear time invariant filters subjected to a nonstationary noise is studied. The two-dimensional power spectrum is defined, and its use for computing the time varying expected power output is illustrated. The derivation of the one-dimensional energy spectrum from the two-dimensional power spectrum is shown. The derivation of the instantaneous power spectrum as the derivative of the truncated energy spectrum is shown. It is concluded that the instantaneous power spectrum is not a useful engineering technique since there are no expressions relating the instantaneous power spectrum at the filter output to that at the input. For the special case in which the nonstationary noise is the product of a modulation function and a stationary noise, it is shown that the problem can often be reduced to an eguivalent stationary problem and solved in a well known way. (Author).
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).
Nonstationarity is another name for intermittency, a phenomenon which affects many physical processes. Data collected in many R&D programs frequently exhibit nonstationary features, and problems inherent in the analysis of such data are profound. The premier objective of these proceedings is to consolidate recent developments in nonstationary analysis. A second objective is to delineate open problems. A by-product will hopefully be a bridging of the gap between related governmental needs, and the present-day research capabilities of both academics and non-academics alike.
