The Wigner Distribution Function with Minimum Spread

Abstract

The Wigner distribution function (WDF) with minimum quadratic spread corresponds to a Gaussian amplitude-modulated waveform with linear frequency- modulation. The optimum WDF is two-dimensional Gaussian and has contours of equal height which are identical to the penalty contours of the quadratic spread measure employed. An alternative measure of spread, involving an exponential reward for concentration, leads to identically the same optimum waveform and WDF. A generalization to a certain class of smoothed WDFs is also possible and is presented The sensitivity of the effective area of a smoothed WDF, to mismatch in shape factor and tilt in the time-frequency plane, is evaluated quantitatively. Keywords: Ellipses; Kernel function; Smoothing.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA199661

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Underwater Systems Center

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Ambiguity
  • Amplitude Modulation
  • Classification
  • Differential Equations
  • Distribution Functions
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Frequency
  • Frequency Modulation
  • Modulation
  • Oceanography
  • Plastic Explosives
  • Security
  • Sensitivity
  • Two Dimensional
  • Universities

Readers

  • Approximation Theory.
  • Radio communications and signal processing.