AbstractNumerical convolution operations, executed on noise contaminated signals, are approximated by FIR digital filters in such a way that the effect of random coloured noise is minimized. Using elementary Hilbert space techniques, the filter functions of certain least‐weighted‐squares digital filters are derived explicitly by the use of discrete orthogonal functions (e.g. Hahn polynomials). the approach is suitable especially for narrowband operations such as smoothing, narrowband differentiation, and narrowband deconvolution (resolution enhancement). Examples of linear‐phase lowpasses with monotone passband, obtained with the aid of Hahn polynomials, are discussed in detail. Also the well‐known maximally flat digital lowpasses which can be derived with the aid of Krawtchouk polynomials, and narrowband differentiators are considered. In the case of least‐weighted‐squares approximation by Hahn polynomials, powerful recursive realizations can be developed to reduce computational r