Structural equivalences in Wave Digital systems based on dynamic scattering cells

In this article we prove that a computable tree-like interconnection of parallel/series Wave Digital adaptors with memory (which are characterized by reflection filters instead of reflection coefficients) is equivalent to a standard (instantaneous) multi-port adaptor whose ports are connected tomutators (2-port adaptors with memory). We prove this by providing a methodology for extracting the memory from a macro-adaptor, which simplifies the implementation of WD structures.