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To study singularities on complex varieties we study Poincar\'e series offiltrations that are defined by discrete valuations on the local ring at thesingularity. In all previous papers on this topic one poses restrictions on thecenters of these valuations and often one uses several definitions forPoincar\'e series. In this article we show that these definitions can differwhen the centers of the valuations are not zero-dimensional, i.e. do not havethe maximal ideal as center. We give a unifying definition for Poincar\'eseries which also allows filtrations defined by valuations that are allnonzero-dimensional. We then show that this definition satisfies a nicerelation between Poincar\'e series for embedded filtrations and Poincar\'eseries for the ambient space and we give some application for singularitieswhich are nondegenerate with respect to their Newton polyhedron.

Poincar\'e series for filtrations defined by discrete valuations with arbitrary center