Wave-variable transformation is a means to maintain stability of haptic teleoperation in the presence of communication time delays. Its drawback is that it affects haptic perception of remote properties and thereby degrades transparency. This paper studies the effect of wave-variable transformation on human haptic perception. Based on a framework of haptic perception developed in previous work, we systematically investigated how the wave variable affects human perception of damping, mass and stiffness properties of an arbitrary linear environment. Both the original wave-variable approach and the generalized wave-variable approach are investigated. Results show how both approaches change human perception of all three mechanical properties of the environment, and how these changes vary with both excitation frequency and time delay. The generalized wave-variable approach on the whole outperforms the original in terms of rendering mass and stiffness, but not always for rendering damping. Results also show that human perception of the dynamics rendered by both approaches is similar to that of the original environment only when time delays are small. As the time delay increases, evaluating the mechanical properties can become very difficult for a human operator if the interaction with the environment is not static.