Multiple-window spectrum estimation (MWSE) is a method of deriving frequency spectra from time series. A set of apodizing windows is applied to the time data and each windowed data set is Fourier transformed. The windows are prolate spheroidal sequences. These form the orthonormal set of functions that is maximally concentrated in both time and frequency domains. An iterative algorithm is then applied to the data set to find a least-squares estimate of the power spectrum. In addition, statistical tests may be applied to determine the existence of periodic components at particular frequencies, their amplitudes, phases, and positions. The method is quantitative and makes no lineshape assumptions. Computer simulations were used to compare MWSE performance with that of conventional Fourier-transform processing with quantification by curve fitting. Signal-to-noise ratio, spectral resolution, linearity, and susceptibility to artifacts were compared. MWSE gives similar signal-to-noise ratio and spectral resolution to Fourier-transform data and is linear over three orders of magnitude but is much more robust with respect to artifacts. In particular, data truncation introduces no baseline distortion, broad baseline humps are removed automatically, and large solvent peaks may be easily removed without affecting adjacent lines. No separate phase correction is required. MWSE gives more accurate quantitative spectra, particularly when the time data are imperfect. The method is, therefore, particularly appropriate for processingin vivodata. The utility of the MWSE method is demonstrated onin vivo1H,31P, and13C NMR spectroscopy data.