Bayesian Spectrum and Chirp Analysis

We seek optimal methods of estimating power spectrum and chirp (frequency change) rate for the case that one has incomplete noisy data on values y(t) of a time series. The Schuster periodogram turns out to be a “sufficient statistic” for the spectrum, a generalization playing the same role for chirped signals. However, the optimal processing is not a linear filtering operation like the Blackman-Tukey smoothing of the periodogram, but rather a nonlinear operation. While suppressing noise/side lobe artifacts, it achieves the same kind of improved resolution that the Burg method did for noiseless data.

[1]  Daniel R. Grischkowsky,et al.  90‐fs tunable optical pulses obtained by two‐stage pulse compression , 1983 .

[2]  朝倉 利光.  R. B. Blackman and J. W. Tukey: The Measurement of Power Spectra, Dover Publications, Inc., New York, 1958, 208頁, 13.5×16cm, $1.85 , 1964 .

[3]  R. Lindsay,et al.  Listening in the Dark , 1958 .

[4]  W. Munk,et al.  Measurements of southern swell at Guadalupe Island , 1957 .

[5]  E. Jaynes.  On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.

[6]  J. P. Burg,et al.  Maximum entropy spectral analysis. , 1967 .

[7]  D. Griffin,et al.  Listening in the Dark , 1959 .

[8]  F. Horner,et al.  Whistlers and Related Ionospheric Phenomena , 1966 .

[9]  E. T. Jaynes,et al.  Survey of the Present Status of Neoclassical Radiation Theory , 1973 .

[10]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[11]  A. Schuster,et al.  On Lunar and Solar Periodicities of Earthquakes , 1897, Nature.

[12]  N. Barber,et al.  The generation and propagation of ocean waves and swell. I. Wave periods and velocities , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[13]  W. J. LeVeque,et al.  WHAT IS THE PROBLEM? , 2019, Paradoxes of Populism.

[14]  Marvin H. J. Guber.  Bayesian Spectrum Analysis and Parameter Estimation , 1988 .

[15]  M. Degroot,et al.  Bayesian Statistics 2. , 1987 .

[16]  S. Gull,et al.  Image reconstruction from incomplete and noisy data , 1978, Nature.

[17]  ARTHUR SCHUSTER.  On Lunar and Solar Periodicities of Earthquakes , 1897, Nature.

[18]  Donald G. Childers,et al.  Modern Spectrum Analysis , 1978 .

[19]  T. Teichmann,et al.  The Measurement of Power Spectra , 1960 .