OPTIMAL PHASE KERNELS FOR TIME-FREQUENCY ANALYSIS


Richard G. Baraniuk

  Department of Electrical and Computer Engineering
  Rice University
  Houston, TX 77005, USA


L. Fridtjof Wisur-Olsen

  Nederlandse Aardolie Maatschappij B.V.
  Royal Dutch Shell
  Schoonebeek, The Netherlands


Abstract:

We consider the design of kernels for time-frequency distributions
through the phase, rather than amplitude, response.  While phase
kernels do not attenuate troublesome cross-components, they can
translate them in the time-frequency plane.  In contrast to previous
work on phase kernels that concentrated on placing the cross-
components on top of the auto-components, we set up a ``don't care''
region and place the cross-components there.  The close connections
between optimal allpass kernels and optimal lowpass kernels provide
new insight into signal-dependent time-frequency analysis.