Jc. Wood et Dt. Barry, RADON TRANSFORMATION OF TIME-FREQUENCY DISTRIBUTIONS FOR ANALYSIS OF MULTICOMPONENT SIGNALS, IEEE transactions on signal processing, 42(11), 1994, pp. 3166-3177
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.