In this paper, we propose a novel generalized S-matrix characterization approach. The goal is to keep track of all observed discontinuities as efficiently as possible. In terms of reflection value, the proposed control strategy is based on transmission coefficients and one-axis rectangular guides. We successfully manipulate metal rectangular waveguide filters with both geometrical and physical discontinuity. Lossless discontinuity is depicted as a periodic structure that contains Metamaterials. The modal development of transverse fields provides the basis for the generalized S-matrix approach. The approach works by breaking down electromagnetic fields for each of the guides that make up the discontinuity on an orthonormal basis. When the Galerkin method is used, the matrix of diffraction of the junction is obtained directly.