Sensitivity of roots to errors in the coefficient of polynomials obtained by frequency-domain estimation methods

Although the roots of a polynomial of high order are extremely sensitive to perturbations in its coefficients, experience has demonstrated that frequency-domain estimation techniques succeed in the determination of accurate poles and zeros, even in the case of high-order transfer function models. The authors prove that this is due to the correlations among the estimated coefficients. When the result of a measurement is a set of correlated values, they conclude that it is not justifiable to use the standard deviation to determine the number of significant digits. Additional digits have to be considered in order to maintain the information enclosed in the correlations.>