Resolving power of spectral matrix filtering: a discussion on the links steering vectors/eigenvectors

Problems of separation of convolutive mixtures of wideband signals impinging on an antenna array of sensors often arise in signal processing. In seismic signal processing, techniques have been developed to perform separation of seismic waves (f-k or median filters, spectral matrix filtering, Radon or Karhunen-Loe`ve transforms, maximum likelihood methods). They give good results in most cases, yet their limits might occur in difficult contexts (waves of very close energies or/and near slowness). The authors analytically study the resolving power of spectral matrix filtering to theoretically explain why the method does not work for waves of close energies. This problem brings one to the question of links between eigenvectors and steering vectors