Time-frequency representation of signals and transformations with respect to time - Application to a radar imagery problem

Analytical techniques are presented for performing time-frequency transformations of narrow band signals to extract meaningful data from radar echoes. The instantaneous spectra are mapped in Hilbert space and treated with a Ville-Wigner function and time-frequency transformations. Affine groups are decomposed into subgroups which are examined for invariants. The narrow-band data extracted carries information on the material of the reflective surface. A Gabor regularization is defined for the time-frequency transformations and is shown to be of use in obtaining a temporal average of the received signal. Finally, application of the method to generating position-color plots of radar targets is demonstrated.