Some History Of The Study Of Higher-order Moments And Spectra

Some of the history of the development of random process higher-moments and spectra is set down for the period preceding 1980. Time-side and frequency-side properties are contrasted. Some uses of the concepts and associated techrriques are mentioned as well as are some of the computational procedures that have been employed.

[1]  J. V. Ness Asymptotic Normality of Bispectral Estimates , 1966 .

[2]  Ya. G. Sinaj On Higher Order Spectral Measures of Ergodic Stationary Processes , 1963 .

[3]  A. Yaglom Einstein's 1914 paper on the theory of irregularly fluctuating series of observations , 1987, IEEE ASSP Magazine.

[4]  SOME REMARKS ON THE SPECTRAL PROPERTIES OF ERGODIC DYNAMICAL SYSTEMS , 1963 .

[5]  M. Hinich,et al.  The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data , 1968 .

[6]  P. Whittle The Analysis of Multiple Stationary Time Series , 1953 .

[7]  A. Shiryaev On Conditions for Ergodicity of Stationary Processes in Terms of Higher Order Moments , 1963 .

[8]  A. Shiryaev Some Problems in the Spectral Theory of Higher-Order Moments. I , 1960 .

[9]  G. W. Kenrick XIX.The analysis of irregular motions with applications to the energy-frequency spectrum of static and of telegraph signals , 1929 .

[10]  M. D. Godfrey AN EXPLORATORY STUDY OF THE BI-SPECTRUM OF ECONOMIC TIME SERIES , 1965 .

[11]  M. Rosenblatt,et al.  Estimation of the Bispectrum , 1965 .

[12]  D. Brillinger An Introduction to Polyspectra , 1965 .

[13]  Theodor Gasser,et al.  System identification, polyspectra and related functions , 1972 .

[14]  M. Rosenblatt Energy transfer for the Burgers’ equation , 1978 .

[15]  A. Yaglom Correlation Theory of Stationary and Related Random Functions I: Basic Results , 1987 .

[16]  Bernard Mazelsky,et al.  Extension of Power Spectral Methods of Generalized Harmonic Analysis to Determine Non-Gaussian Probabilitv Functions of Random Input Disturbances and Output Responses of Linear Systems , 1954 .

[17]  Homi Jehangir Bhabha On the stochastic theory of continuous parametric systems and its application to electron cascades , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  T. Madden Spectral, Cross-Spectral, and Bispectral Analysis of Low Frequency Electromagnetic Data , 1964 .

[19]  Geoffrey Ingram Taylor,et al.  Diffusion by Continuous Movements , 1922 .

[20]  M. Rosenblatt,et al.  Bispectral measurements in turbulence , 1976, Journal of Fluid Mechanics.

[21]  I. G. Zhurbenko,et al.  On the Estimation of Mixed Semi-Invariants for a Certain Class of Random Processes , 1970 .

[22]  Alladi Ramakrishnan,et al.  Stochastic processes relating to particles distributed in a continuous infinity of states , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[23]  Leo J. Tick,et al.  The Estimation of “Transfer Functions” of Quadratic Systems , 1961 .

[24]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[25]  D. Brillinger Comparative Aspects of the Study of Ordinary Time Series and of Point Processes , 1978 .

[26]  M. Rosenblatt,et al.  REMARKS ON HIGHER ORDER SPECTRA , 1964 .