TOMOGRAPHIC TIME-FREQUENCY ANALYSIS AND ITS APPLICATION TOWARD TIME-VARYING FILTERING AND ADAPTIVE KERNEL DESIGN FOR MULTICOMPONENT LINEAR-FM SIGNALS

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.