This article is concerned with the quantised H filtering problem for discrete-time systems. The quantiser considered here is dynamic and composed of a dynamic scaling and a static quantiser. Motivated by practical transmission channels requirements, the static quantiser ranges are fully considered in this article. A quantised H filter design strategy is proposed, taking quantiser errors into account, where a convex optimisation method is developed to minimise static quantiser ranges with meeting H performance requirement for quantised augmented systems. A numerical example is given to illustrate the effectiveness of the proposed filter design method.