RADON TRANSFORMATION OF TIME-FREQUENCY DISTRIBUTIONS FOR ANALYSIS OF MULTICOMPONENT SIGNALS

The Radon transform of a time-frequency distribution produces local ar eas of signal concentration that facilitate interpretation of multicom ponent signals. The Radon-Wigner transform can be efficiently implemen ted with dechirping in the time domain, however, only half of the poss ible projections through the time-frequencpy plane can be realized bec ause of aliasing. We show here that the frequency dual to dechirping e xists, so that all of the time-frequency plane projections can be calc ulated efficiently. Both time and frequency dechirping are shown to wa rp the time-frequency plane rather rotating it, producing an angle dep endent dilation of the Radon-Wigner projection axis. We derive the dis crete-time equations for both time and frequency dechirping, and highl ight some practical implementation issues. Discrete dechirping is show n to correspond to line integration through the extended-discrete, rat her than the discrete, Wigner-Ville distribution. Computationally, dec hirping is O(2N log 2N) instead of O(N-3) for direct projection, and t he computation is dominated by the fast Fourier transform calculation. The noise and cross-term suppression of the Radon-Wigner transform ar e demonstrated by several examples using dechirping and using direct R adon-Wigner transformation.