Waveguide digital filters were derived by sampling ideal waveguide networks with respect to space and time. It was shown that the DWF can be transformed into well known ladder and lattice digital filter structures simply by pushing delays around to the bottom rail (in the special case of a cascade, reflectively terminated chain of waveguides). The DWF structure gives a precise implementation of physical wave phenomena in time-varying media; consequently, waveguide filters are useful as building blocks for computational models of acoustic systems.