WIGNER-BASED FORMULATION OF THE CHIRPLET TRANSFORM


Richard G. Baraniuk 

  Department of Electrical and Computer Engineering
  Rice University
  Houston, TX 77251-1892

Douglas L. Jones 
  Department of Electrical and Computer Engineering
  University of Illinois
  Urbana, IL 61801


Using the Wigner distribution, we derive and analyze a matrix
formulation for the chirplet transform, a signal analysis tool that
generalizes the wavelet and short-time Fourier transforms.  The
formulation expresses the translations, scalings, and shears of the
chirplet transform in terms of affine matrix transformations on the
time-frequency plane.  Our approach leads naturally to several new
signal transforms, which we derive, analyze, and extend.