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This invention provides a method and system for reconstructing the full-band electrochemical impedance spectroscopy (EIS) of lithium-ion batteries. The method includes: performing distributed relaxation time (DRT) analysis on each group of battery EIS samples to obtain DRT spectra; aligning the DRT spectra on the logarithmic time constant axis and performing ensemble statistics, selecting peaks and / or valleys that stably appear under multiple operating conditions based on statistical stability, and mapping them to obtain a set of conditionally invariant characteristic frequencies; selecting characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and performing sparse EIS measurements on the target battery at these characteristic frequency points to obtain sparse complex impedance inputs; generating a full-band complex impedance sequence based on the sparse complex impedance inputs using an autoregressive reconstruction model; and performing battery state estimation and fault diagnosis based on the full-band complex impedance sequence. This invention significantly improves the continuity of the spectral shape and the generalization ability across operating conditions under sparse sampling conditions, while reducing the full-spectrum testing time and sampling burden.