Dithering the coefficients of digital filters enhances the selection of available transfer functions when the coefficient word length is limited. Furthermore, dithering can reduce limit cycle oscillations. However, noise is introduced into the filter. This paper presents a novel analytic technique for determining the noise components introduced by dithering. It uses time-squared transfer functions to produce generalised expressions for the introduced noise. These expressions increase the potential for exploiting the advantages of randomly dithering coefficients in digital filters. Furthermore, the analysis can be applied to continuous systems.