Computation of linear filter networks containing delay-free loops, with an application to the waveguide mesh

A method that computes linear digital filter networks containing delay-free loops is proposed. Compared to existing techniques the proposed method does not require a rearrangement of the network structure, conversely it makes use of matrices describing this structure and specifying the connections between the filter blocks forming the network. For this reason the efficiency of the method becomes interesting when the filter blocks are densely interconnected. The Triangular Waveguide Mesh is an example of "dense" filter network: Using the proposed method we can compute a transformed, delay-free version of this mesh, obtaining simulations that are significantly more accurate compared to those provided by the traditional, explicitly computable formulation of the triangular mesh.