A recursive fixed-memory filter is developed to fit a first-order polynomial to equally spaced measurements. The parameters of the filter are determined using a weighted least-squares performance index. The recursive and the nonrecursive realisations of the fixed-memory filter are compared, and the effects of the weighting coefficient on stability, noise performance and frequency response are discussed. It is shown that, by a proper selection of the weighting coefficient, the performance of the filter is improved.