Impulse Response Estimation via Laguerre-Fourier Expansion

What the math gives to ML

The paper replaces direct frequency-domain deconvolution, which divides by potentially vanishing input spectra, with a Laguerre-Fourier coordinate system and a circulant FFT-solvable formulation. The transferable asset is not the system-identification application itself, but the use of a stable, structured basis for representing long causal impulse responses together with FFT-based convolution and explicit conditioning control. A promising neural-network adaptation is a causal sequence layer whose long convolution kernel is parameterized by a small number of Laguerre coefficients, optionally initialized or regularized using the input spectrum, rather than learning every lag independently. This can provide compact long-memory dynamics while avoiding unstable high-frequency or near-zero spectral directions.