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Pseudowhitening of oversampled signals in range is proposed as a method to improve the performance of spectral moment and polarimetric variable estimators on weather surveillance radars. In an attempt to overcome the noise sensitivity of the whitening transformation, a solution based on the minimum mean-square-error criterion is considered first; however, this transformation is less practical than whitening because it requires knowledge of the signal-to-noise ratio at every range location. Pseudowhitening techniques are introduced as practical solutions that achieve a suboptimal compromise between variance reduction and noise sensitivity. Based on regularization methods for the solution of ill-conditioned problems, two pseudowhitening schemes are proposed: the clipped singular value decomposition transformation and the sharpening filter. By comparing their statistical performance with theoretical minimum bounds, it is shown that pseudowhitening-based estimators are almost optimal under practical conditions. Estimators based on pseudowhitening techniques avoid the pitfalls of their whitening-transformation-based counterparts and lead to more accurate radar products and/or rapid data acquisition for a much wider range of signal-to-noise ratios.