Application of eigenanalysis and tomography to time-frequency representations

The author addresses the question of how to obtain the high accuracy inherent in Wigner representations while avoiding the artifacts caused by cross products between multiple signal components. One approach involves separation of the components of a multicomponent signal by means of eigenanalysis. Various distortions are deliberately introduced by differentiation, smoothing, and the use of time varying gains so as to increase the rank of the signal autocovariance matrix. Separate Wigner distributions of the principal eigenvectors of this matrix are weighted by the eigenvalues and added. The filtering/synthesis problem is automatically solved, since different eigenvectors approximate individual signal components. Another approach is to form inner products of the signal with time functions that have line-like Wigner distributions, thus constructing projection samples that can be used to obtain the signal distribution by means of Radon transform inversion. The tomographic technique can completely eliminate cross-product effects with little loss of accuracy.<>