We propose an n-order noise, which is realized by driving an n-order linear differential equation with a Gaussian white noise. The time-derivative noise is a low-resistant band-passing noise. If the derivative noise is regarded as a thermal one, the system has a vanishing effective friction and it should induce ballistic diffusion of a free particle at long times. The simulation method for the generalized Langevin equation driven by the n-order noise is discussed systematically. The features of three-order derivative noises are presented when they are applied to a ratchet system.