Reciprocity,inter-reciprocity,and transposition in wave digital filters

For wave digital filters, basic theorems which, although being more general, have a similarity to the difference form of Tellegen's theorem for classical networks, are derived, and the properties of reciprocity and inter-reciprocity are defined. To each wave digital filter, there corresponds an entire family of transposed wave digital filters; each of these is inter-reciprocal with the original one. Two types of transposition, called intrinsic and elementary transposition, are of particular importance. For these, the number of multipliers is the same after transposition as before, which is of interest for obtaining equivalent realizations. Intrinsic and elementary transposition are related to transposition (in the classical sense) and duality in the reference filter from which the wave digital filter is derived.