Impulse Response Estimation via Laguerre-Fourier Expansion

[2608.14769] Impulse Response Estimation via Laguerre-Fourier Expansion Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Electrical Engineering and Systems Science > Signal Processing arXiv:2608.14769 (eess) [Submitted on 14 Aug 2026] Title: Impulse Response Estimation via Laguerre-Fourier Expansion Authors: Tamás Dózsa , Art J. R. Pelling , Matthias Voigt View a PDF of the paper titled Impulse Response Estimation via Laguerre-Fourier Expansion, by Tam\'as D\'ozsa and 2 other authors View PDF HTML (experimental) Abstract: The empirical transfer function estimate (ETFE) is a widely used method for system identification of linear time-invariant (LTI) systems in engineering disciplines such as acoustics, audio engineering, seismography, and tomography. However, ETFE suffers from numerical limitations when the excitation signal is band-limited or vanishes at certain frequencies, which is a common physical constraint of the excitation in practice. In such cases, division in the frequency domain becomes heavily ill-conditioned, and small measurement disturbances or numerical inaccuracies can degrade the solution. This paper presents L-ETFE, a generalization of ETFE based on Laguerre-Fourier expansions that addresses these limitations. After a suitable transformation, the method can yield a well-conditioned circulant problem even when the original ETFE system is ill-conditioned. Solving this problem via classical ETFE yields the discrete Laguerre-Fourier coefficients of the system's transfer function. The desired impulse response (IR) of the system-to-be-identified can then be recovered by a subsequent transformation pipeline. We derive novel and efficient algorithms for performing these transformations and analyse the conditioning of the transformed problem, explicitly characterizing its dependence on the input and a parameter used in the Laguerre-Fourier expansion. We evaluate the method on two simulated discrete-time LTI systems of varying complexity. The experiments demonstrate accurate IR recovery for spectral-zero and band-limited excitation, where standard ETFE fails. Subjects: Signal Processing (eess.SP) ; Complex Variables (math.CV); Dynamical Systems (math.DS) MSC classes: 93B30, 33C45, 94A12, 65T50 Cite as: arXiv:2608.14769 [eess.SP] (or arXiv:2608.14769v1 [eess.SP] for this version) https://doi.org/10.48550/arXiv.2608.14769 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Art J. R. Pelling [ view email ] [v1] Fri, 14 Aug 2026 14:20:01 UTC (11,075 KB) Full-text links: Access Paper: View a PDF of the paper titled Impulse Response Estimation via Laguerre-Fourier Expansion, by Tam\'as D\'ozsa and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: eess.SP < prev | next > new | recent | 2026-08 Change to browse by: eess math math.CV math.DS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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