While nonlinear filtering for circular quantities is closely related to nonlinear filtering on linear domains, the underlying manifold enables the development of novel filters that take advantage of the boundedness of the domain. Previously, we introduced Fourier filters that approximate the density or its square root using Fourier series. For these filters, we proposed filter steps for arbitrary likelihoods and prediction steps for the identity system model with additive noise. This paper adds the capability of handling arbitrary transition densities in the prediction step, which facilitates, e.g., the use of the filters for nonlinear systems with additive noise. In the evaluation, the new prediction steps for the Fourier filters outperform an SIR particle filter, a grid filter, and a nonlinear variant of the von Mises filter.