On the robustness of exponential base terms and the Padé denominator in some least squares sense

Citation

Knaepkens F & Cuyt A (2023) On the robustness of exponential base terms and the Padé denominator in some least squares sense. Numerical Algorithms, 92 (1), pp. 747-766. https://doi.org/10.1007/s11075-022-01455-z

Abstract
The exponential analysis of 2n uniformly collected samples from an n-term exponential sum is equivalent to the reconstruction of a rational function of degree n −1 over n. The latter is by computing the Padé approximant of the z-transform of the sequence of samples. In practice, the samples are often noisy and 2n is replaced by N > 2ν with ν > n, leading to a least squares computation of the Padé approximant of degree ν −1 over ν. We show that the latter is a perturbed version of the one of degree n −1 over n and that the n exponential base terms can still be retrieved reliably. This has remained an open problem for many years, despite the fact that the least squares computation was used in most applications.

Keywords
Exponential analysis; Pade approximation; Perturbation analysis; Conditioning; Robustness

Journal
Numerical Algorithms: Volume 92, Issue 1