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The rotation velocities of galaxies are estimated from their HI profile widths at a percentage of their peak intensities. While smoothing low S/N ratio spectra improves widths estimated from them, binning usually limits the attainable precision from well observed spectra. Two effects occur. The first comes from the finite resolution of a bin, and is ameliorated by higher resolution; the second comes from the exact positioning of a set of bins with respect to the signal, and dominates estimation errors for the 50% (20%) width of the usual 8 km/s resolution spectra at a S/N >30 (5), though its influence is easily removed by rebinning.
We simulate the estimation process in the presence of noise, and use a FT rebinning algorithm to find that the resulting variance of a width estimate is proportional to (N/S) down to a precision ³10E-5 of a bin at a S/N Å10E6: the exact numerical factors depend on both resolution and the functional form of the spectral edge. The question then arises, as to the optimal resolution needed to observe galaxy widths to resolution indep- endent precisions of 1 and 0.1 km/s. The most demanding spectra come from Sc galaxies, such as UGC5646, with narrow, intense peaks. These exhibit rounded peaks at a 2 km/s resolution, with about 5 channels across their tops: used as kernels with a rebinning algorithm these show that an 8 km/s resolution suffices to determine unbiased widths to <1 km/s, but 4 km/s resolution is needed to reliably reach a precision of <0.1 km/s. This is in practise the resolution needed to Nyquist sample the intrinsic shape of an integrated HI profile. However, an observer retains greater flexibility if all precision observations are made at about 2 km/s resolution. This allows (i) unexpected discontinuities in profile edges to be detected; (ii) the use of smoothing operations over the likely range of S/N ratios to completely restore channel to channel precision lost in the use of a higher resolution; (iii) surety that integration time gives the only limit to achieved precision.
