Radon transformation of time-frequency distributions for analysis of multicomponent signals

The Radon transform of a time-frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals. The Radon-Wigner transform can be efficiently implemented with dechirping in the time domain, however, only half of the possible projections through the time-frequency plane can be realized because of aliasing. We show here that the frequency dual to dechirping exists, so that all of the time-frequency plane projections can be calculated efficiently. Both time and frequency dechirping are shown to warp the time-frequency plane rather rotating it, producing an angle dependent dilation of the Radon-Wigner projection axis. We derive the discrete-time equations for both time and frequency dechirping, and highlight some practical implementation issues. Discrete dechirping is shown to correspond to line integration through the extended-discrete, rather than the discrete, Wigner-Ville distribution. Computationally, dechirping is O(2N log 2N) instead of O(N³) for direct projection, and the computation is dominated by the fast Fourier transform calculation. The noise and cross-term suppression of the Radon-Wigner transform are demonstrated by several examples using dechirping and using direct Radon-Wigner transformation