In a number of physical problems such as the motion of vehicles travelling over rough ground or the noise emanating from a moving source, non-stationarity is induced by a non-linear time dilation (due to velocity variations or Doppler effects) of the source or excitation process so that the resulting process is “frequency modulated”. This is true even if the underlying process is homogeneous in another domain. Hitherto it has not been possible to apply the frequency/time analysis due to Priestley [1] to this class of problem but here, by introducing the concept termed “covariance equivalence” by the authors, this method can be seen to apply. An example of a vehicle moving with variable velocity on a rough surface is considered.