Wave digital filters are a class of digital filters. They are equivalent to commensurate transmission line circuits synthesized with uniform, lossless, and commensurated transmission lines. In order to extend their applications to physical wave phenomena including quantum electronics, it is necessary to consider a generalized distributed line whose velocity of energy flow has frequency characteristics. This paper discusses a generalized distributed circuit, and we obtain two types of lines, lossless and cut-off. In order to analyze these lines, we discuss signal flow graphs of steady state voltage and current. The reflection factors we obtain here are the same as that for an active power or a diagonal element of a scattering matrix, which is zero in conjugate matching. By using this reflection factor, we obtain band-pass filters synthesized with the cut-off lines. We also describe an analysis method for nonuniform line related to Riccati differential equation.