In this article, we introduce novel filter design conditions for discrete-time linear parameter-varying (LPV) systems. The two main features of the proposed conditions are: the ability of handling LPV systems subject to variation in all matrices of the system and the generalization for systems with bounded rates of parameter variation. Filter stability and H-infinity filtering problems are addressed through poly-quadratic Lyapunov functions in terms of linear matrix inequalities. Numerical examples illustrate the proposed designs effectiveness.