Different software packages are available commercially which can be applied to oscillatory shear data to recover an estimate of the relaxation spectrum of the viscoelastic material tested. The underlying algorithms, based on some form of regularization, are indirect and technically involved. Davies and Anderssen [J. Non-Newtonian Fluid Mech. 73, 163-179 (1997)] have derived exact sampling localization results for the determination of elastic moduli from (exact) storage and loss moduli. It is now shown how their results can be exploited to construct simple and explicit moving-average formulae which recover estimates of the relaxation spectrum from oscillatory shear data, with realistic observational errors. Explicit moving-average formulae are presented which experimentalists can apply immediately to appropriately sampled oscillatory shear measurements. The given formulae are validated on noisy data obtained from synthetic relaxation spectra. (C) 2001 The Society of Rheology.