Spectral and time-domain data representations in measurements

Abstract

Classic stationary models and spectral representations of data are commonly used in practice, but they are not sufficient for solving modern problems of data processing in measurements. There are some kinds of non-stationary models, which are based on generalized spectral representations. Besides, some classes of time-domain representations are studied for non-stationary random functions. In the paper spectral and time-domain representations are compared in some aspects, including field of application, and efficiency for data processing in measurements. Regarding generalized spectral models, harmonizable processes and random processes with stationary increments are considered. The latter group seems to be especially useful for measurement problems. It is much wider, than the set of stationary processes, but these processes also have spectral representations. The extended model enables one to develop spectral methods of data processing, and also permits to investigate new data characteristics. For instance, Allan variance, which is widely used nowadays, is the estimate of structure function within this model.As regards time-domain models, general canonical representations of the processes are considered, which may possess any spectral type and multiplicity. However, one-dimensional processes, which are used in practice, have multiplicity one.