Jc. Wood et Dt. Barry, TOMOGRAPHIC TIME-FREQUENCY ANALYSIS AND ITS APPLICATION TOWARD TIME-VARYING FILTERING AND ADAPTIVE KERNEL DESIGN FOR MULTICOMPONENT LINEAR-FM SIGNALS, IEEE transactions on signal processing, 42(8), 1994, pp. 2094-2104
Since line integrals through the Wigner spectrum can be calculated by
dechirping, calculation of the Wigner spectrum may be viewed as a tomo
graphic reconstruction problem. In this paper, we show that all time-f
requency transforms of Cohen's class may be achieved by simple changes
in backprojection reconstruction filtering. The resolution/cross-term
tradeoff that occurs in time-frequency kernel selection is shown to b
e analogous to the resolution-ringing tradeoff that occurs in computed
tomography (CT). ''Ideal'' reconstruction using a purely differentiat
ing backprojection filter yields the Wigner distribution, whereas low-
pass differentiating filters produce cross-term suppressing distributi
ons such as the spectrogram or the Born-Jordan distribution. It is als
o demonstrated how this analogy can be exploited to ''tune'' the recon
struction filtering (or time-frequency kernel) to improve the ringing/
resolution tradeoff. Some properties of the projection domain, which i
s also known as the Radon-Wigner transform, are characterized, includi
ng the response to signal delays or frequency shifts and projection ma
sking or convolution. Last, time-varying filtering by shift-varying co
nvolution in the Radon-Wigner domain is shown to yield superior result
s to its analogous Cohen's class adaptive transform (shift-invariant c
onvolution) for the multicomponent, linear-FM signals that are investi
gated.