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:

$P\left(x;T\right)=\frac{1}{T}{\int }_{0}^{T}x{\left(t\right)}^{2}\cdot \mathrm{d}t$ (A8.1)

(A8.1)

For the example ...

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