Error analysis of signal zeros: a projected companion matrix approach

An error analysis of so-called signal zeros of polynomials associated with exponentially damped/undamped signals is performed and zero error bounds are derived. The bounds are in terms of the angle between the exact and approximate signal subspace, the signal parameter themselves, the polynomial degree, and the error on the polynomial coeficients. The key idea behind the analysis is to regard signal zeros as eigenvalues of projected companion matrices and then to generate error bounds by exploiting perturbation theorem for eigenvalues. The conclusion drawn from the bounds is that the signal zeros become relatively insensitive to small perturbations on the polynomial coefficients as long as the polynomial degree is large enough and the zeros are extracted as eigenvalues of projected companion matrices. Also, the bounds suggests that signal zero estimates derived from projected companion matrices are more accurate than those obtained from the companion matrices themselves. Illustrative numerical results are provided.