Discrete filters are used in numerous digital signal processing applications and numerical simulations, for anti-aliasing, de-noising, and post-processing. Our specific interest is for application in large-eddy simulations. In this work, we investigate analytically the reconstruction properties of different filters, and how their discrete approximations using different rules affect the convergence and accuracy of the reconstructed signal. Following this analysis, a constrained and adaptive optimisation framework is proposed for the automated calculation of explicit forward but also direct-inverse discrete filter coefficients for a given filter transfer function. The optimised forward filters are shown to perform well with stable reconstruction using classic van Cittert iterations. The optimised direct-inverse filters eliminate the need to apply any iterations thereby substantially reducing the computational cost required for reconstruction which is one of the main challenges associated with deconvolutionbased modelling in large-eddy simulations.