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T.A.C.M. Claasen, W.F.G. Mecklenbräuker:
"On the Transposition of Linear Time-Varying Discrete-Time Networks and its Application to Multirate Digital Systems";
Philips Journal of Research, 33 (1978), 1/2; 78 - 102.

Time-varying discrete-time networks are considered and their description by means of a transmission function is given. Such a description can be applied to discrete-time networks which contain e.g. modulators and subsystems operating at different sampling rates. Two forms of Tellegen's theorem are derived for these networks. Each of these forms suggests a definition of transposition, called hermitian transpose and generalized transpose, respectively. The generalized transpose can be seen as a generalization of the transposition concept defined for time-invariant networks which it includes as a special case. For networks with real parameters the two transposition concepts are the same, but hermitian transposition has certain advantages for systems with complex parameters. At transposition theorem is discussed that relates the transmission function of either form of transpose network to that of the original network. As an application of this theorem, a sensitivity analysis is given. Finally, an extension of the foregoing theory is discussed for networks containing both analog and digital parts.

tansposition; time-varying networks; different sampling rates; Tellegen's theorem; discrete-time

http://publik.tuwien.ac.at/files/PubDat_249743.pdf