The determination of transport coefficients through the time-honoured Green-Kubo theory of linear response and equilibrium molecular dynamics requires significantly longer simulation times than those of equilibrium properties, while being further hindered by the lack of well-established data-analysis techniques to evaluate the statistical accuracy of the results. Leveraging recent advances in the spectral analysis of the current time series associated to molecular trajectories, we introduce a new method to estimate the full (diagonal as well as off-diagonal) Onsager matrix of transport coefficients from a single statistical model. This approach, based on the knowledge of the statistical distribution of the Onsager-matrix samples in the frequency domain, unifies the evaluation of diagonal (conductivities and viscosities) and off-diagonal (e.g., thermoelectric) transport coefficients within a comprehensive framework, significantly improving the reliability of transport coefficient estimation for materials ranging from molten salts to solid-state electrolytes. We validate the accuracy of this method against existing approaches using benchmark data on molten cesium fluoride and liquid water, and conclude our presentation with the computation of various transport coefficients of the Li₃PS₄ solid-state electrolyte.