This group is interested in a variety of problems in statistical communication theory. Our current research is concerned primarily with: measurement of correlation functions , location of noise sources in space by correlation methods, statistical behavior of coupled oscillators, nonlinear feedback systems, stochastic approximation methods in the analysis of nonlinear systems, measurement of the kernels of a nonlinear system, a problem in radio astronomy, and factors that influence the recording and reproduction of sound. 1. The measurement of the first-order and second-order correlation functions by means of orthogonal functions is being studied. Of primary concern are the measurement errors resulting from the truncation of the orthogonal set and from the use of finite time of integration. 2. Noise sources in space can be located by means of higher-order correlation functions. A study is being made of the errors, caused by finite observation time, in locating sources by this method. 3. Many physical processes may be phenomenologically described in terms of a large number of interacting oscillators. A study of these processes is producing some interesting results. 4. The design of a control system can be considered as a filtering problem with constraints imposed by fixed elements. By combining the functional power series and the differential equation methods of system characterization a formal solution to the problem can be found. Research is being conducted to determine the restrictions on the desired filtering operation and fixed elements that are necessary to achieve a practical system configuration. 5. Stochastic approximation methods have been considered for proving the convergence of certain iterative methods of adjusting the parameters of a system. The adjustment seeks to minimize the mean of some convex weighting function of the error. An investigation is being made of the types of systems and signals to which the methods are applicable. 6. A nonlinear system can be characterized by a set of kernels of all orders. The measurement of these kernels is a major problem in the theory of nonlinear systems. A method of measurement that depends upon crosscorrelation functions has been developed. Research on this problem is concerned primarily with the development of techniques that involve tape recording and digital computation, and the application of the method to various problems. 7. A project has been initiated that will have as its goal the measurement of the galactic deuterium-to-hydrogen abundance ratio. The approach to this problem will be based upon digital correlation …
[1]
N. Wiener,et al.
Nonlinear Problems in Random Theory
,
1964
.
[2]
W. Rudin.
Principles of mathematical analysis
,
1964
.
[3]
H. J. Zimmermann,et al.
QUARTERLY PROGRESS REPORT NO. 53
,
1959
.
[4]
L. J. Chu.
Physical Limitations of Omni‐Directional Antennas
,
1948
.
[5]
A. Viterbi.
Phase-locked loop dynamics in the presence of noise by Fokker-Planck techniques
,
1963
.
[6]
John Nathaniel Harris,et al.
Digital transistor circuits
,
1966
.
[7]
J. Y. Hayase,et al.
Properties of second-order correlation functions
,
1957
.
[8]
U. Grenander.
Stochastic processes and statistical inference
,
1950
.
[9]
Amar G Bose,et al.
A theory of nonlinear systems
,
1956
.
[10]
Martin B. Brilliant,et al.
Theory of the analysis of nonlinear systems
,
1958
.
[11]
V. E. Benes,et al.
Statistical Theory of Communication
,
1960
.
[12]
Simon Ramo,et al.
Fields and waves in modern radio
,
1944
.
[13]
M. Schetzen.
Measurement of correlation functions
,
1964
.
[14]
Henry E Singleton.
Theory of nonlinear transducers
,
1950
.
[15]
C. Shannon.
Probability of error for optimal codes in a Gaussian channel
,
1959
.
[16]
N. Wiener.
The Fourier Integral: and certain of its Applications
,
1933,
Nature.
[17]
R. Booton.
An Optimization Theory for Time-Varying Linear Systems with Nonstationary Statistical Inputs
,
1952,
Proceedings of the IRE.