ABSTRACT
This chapter examines the stability problem of the standard Padé approximant (PA) for unambiguously identifying both the genuine and spurious roots by the analytical procedure of Holtz and Leondes. Noise poles can be on either side of the unit circle appearing as mixed with or separated from the genuine poles. When they are on the ‘wrong’ side of the unit circle, noise poles will be regularized along with the like portion of the genuine harmonics from input data. Regularization does not mean elimination of spurious roots, but rather their reflection to the physical side of the unit circle, so that all the harmonics are exponentially damped. The chapter derives an expression showing that the power spectrum in the Padé–Schur approximant (PSA) is invariant under the constrained root reflection. The final working formula for the power spectrum computed by the PSA contains no spurious roots at all and this is true for both the numerator and the denominator polynomials.
