Wigner distribution and FM radar signal design

The Wigner distribution is a bilinear distribution originally developed in the field of quantum mechanics. It has recently attracted considerable attention as a time-frequency distribution for use in signal processing. The properties of the Wigner distribution are reviewed and its relationship to other distributions, in particular the ambiguity function, is described. Wigner distributions for frequency-modulated pulse-compression radar signals are presented and the effect of Doppler shift is demonstrated. Its use in the design of radar signals is discussed. The Wigner distribution provides an elegant way of qualitatively describing the effects of Doppler shift in pulse-compression radar, but is unlikely to provide a basis for the design of frequency-modulated radar signals.

[1]  H. L. Grubin,et al.  The Wigner Distribution Function , 1982 .

[2]  Charles A. Stutt,et al.  Some results on real-part/imaginary-part and magnitude-phase relations in ambiguity functions , 1964, IEEE Trans. Inf. Theory.

[3]  August W. Rihaczek,et al.  Signal energy distribution in time and frequency , 1968, IEEE Trans. Inf. Theory.

[4]  Françoise Peyrin,et al.  A unified definition for the discrete-time, discrete-frequency, and discrete-time/Frequency Wigner distributions , 1986, IEEE Trans. Acoust. Speech Signal Process..

[5]  Charles E. Cook,et al.  Radar Signals: An Introduction to Theory and Application , 1967 .

[6]  Philip M. Woodward,et al.  Probability and Information Theory with Applications to Radar , 1954 .

[7]  Alan S. Gevins,et al.  Wigner Distributions of Human Event-Related Brain Potentials , 1986, IEEE Transactions on Biomedical Engineering.

[8]  T. Claasen,et al.  THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS , 1980 .

[9]  T. Claasen,et al.  The aliasing problem in discrete-time Wigner distributions , 1983 .

[10]  A. C. Fairhead,et al.  Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses , 1986 .

[11]  Leon Cohen,et al.  Positive time-frequency distribution functions , 1985, IEEE Trans. Acoust. Speech Signal Process..

[12]  Steven M. Sussman,et al.  Least-square synthesis of radar ambiguity functions , 1962, IRE Trans. Inf. Theory.

[13]  B. V. K. Vijaya Kumar.  Role Of Wigner Distribution Function In Pattern Recognition , 1985, Other Conferences.

[14]  R. F. O'Connell,et al.  The Wigner distribution function—50th birthday , 1983 .

[15]  J. Klauder,et al.  The theory and design of chirp radars , 1960 .

[16]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

[17]  L. Cohen.  Generalized Phase-Space Distribution Functions , 1966 .

[18]  M. Scully,et al.  Distribution functions in physics: Fundamentals , 1984 .

[19]  P. M. Woodward.  3 – INFORMATION THEORY , 1953 .

[20]  A.I. Sinsky,et al.  Standardization of the Definition of the Radar Ambiguity Function , 1974, IEEE Transactions on Aerospace and Electronic Systems.

[21]  Thomas W. Parks,et al.  Time-varying filtering and signal estimation using Wigner distribution synthesis techniques , 1986, IEEE Trans. Acoust. Speech Signal Process..

[22]  Martin J. Bastiaans,et al.  Use Of The Wigner Distribution Function In Optical Problems , 1985, Other Conferences.

[23]  Bahaa E. A. Saleh,et al.  Time-variant filtering of signals in the mixed time frequency domain , 1985, IEEE Trans. Acoust. Speech Signal Process..