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2014 Reprint of 1962 Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. The present volume deals with the theory of stationary random functions, and contains indispensable background material for an understanding of such diverse topics as turbulence theory, the theory of servomechanisms and information theory. The approach is intuitive, stressing physical interpretation of the results obtained. Part I discusses the general theory of stationary random functions. Part II is devoted to the Wiener-Kolmogorov theory of extrapolation and interpolation of random sequences and processes, with an exhaustive treatment of rational spectral densities, the case of paramount practical importance. Detailed solutions are given, based on the use of complex variable techniques.