Two types of integral equations have been used in the literature to estimate the parameters of a continuous-time model of a linear system. This paper reveals the relationships between them and outlines the method of removing initial conditions. It then considers discrete approximations of signals and multiple integrals occurring in these equations. New recursive formulae are given for integrals of both types with samples and the so-called ‘block-pulse coefficients’ or averaged measurements. This implies that the methods developed using the block-pulse function approach with integral equation models can be extended easily with samples and vice versa.