Determining the passive region of the multirate wave transform on the practical implementation

This paper proposes a computation scheme for determining parameters guaranteeing passivity of a haptic interface with the multirate wave transform (MWT). A practical implementation of MWT considering unit time delays is presented and a passivity condition is obtained from the scattering matrix. Parameter ranges guaranteeing passivity of a haptic interface with MWT are obtained from the extreme case study of the proposed passivity condition. Various simulations and experiments have shown that stable force displays can be achieved with the proposed parameter values.