Sensitivity eigenanalysis for single shift-invariant subspace-based methods

A signal eigenvalue sensitivity analysis for subspace-based methods that exploit the shift-invariance property present in the signal subspace is considered. It is proved that signal eigenvalues are rather insensitive to small perturbations in the data provided the dimension of the problem is large enough and the eigenvalues themselves are not extremely close to each other. In addition, bounds on the signal eigenvalue error that depend on both the largest canonical angle between the exact and approximate signal subspace and the dimension of the data matrix are provided. The theory is illustrated by a numerical example where a signal taken from the literature is analysed. ( 2000 Elsevier Science B.V. All rights reserved.