Essentials of Vehicle Dynamics

Appendix 8

The Power Spectral Density

Let x(t) be a real-valued signal derived from the behavior of a system in time. For a vehicle–driver system, x(t) could be the steering angle or the vertical position of the vehicle body. The energy, related to x(t), is proportional to x(t)². For the vehicle body, the square of the vertical position is proportional to the energy stored in the suspension, due to road disturbances. For a driver, the square of the steering angle corresponds to the energy that is being delivered by the driver to steer the vehicle. The corresponding average power P(x;T) over a time interval with length T can be expressed as the summation of the supplied energy per unit of time:

$P(x;T)=\frac{1}{T}{\int }_0^{T}x{(t)}^2\cdot \mathrm{d}t$ (A8.1)

(A8.1)

For the example ...