A fundamental property of every pair of radar units is their compatibility with respect to frequency measurements. More precisesly, one has the following definition:
Two radar units are said to be Fourier compatible if and only if a continuous wave train emitted by one radar unit produces a return signal which has a sharp Fourier spectrum at the second radar unit. If the return signal is not spectrally sharp (within prespecified bounds), then the two units are said to be Fourier incompatible.
A pair of Fourier compatible radar units, say A and B, is characterized by two frequency shift factors. The transmission process A B is characterized by
The numbers and are, of course, the familiar Doppler frequency shift factors if A and B are freely floating units, and the pseudo-gravitational frequency shift factors if A and B are uniformly and collinearly accelerated units. For the former one has , while for the latter one has .
These frequency shifts (``Fourier compatibility factors'') are strictly kinematical aspects of A and B. They involve neither the inertia nor the dynamics of material particles. Nevertheless, they do distinguish between free-float and acceleration. Indeed this distinction is encoded into the the relation between the frequency shifts associated with the reflection process A B A for monochromatic radiation. There one has
For example, it is clear that all freely floating (``inertial'') units are Fourier compatible. So are the units which are linearly and uniformly accelerated and have the same future and past event horizons. However, an accelerated unit and one in a state of free float are not Fourier compatible. Neither are two units if one of them undergoes non-uniform acceleration. Such units measure a Doppler chirp instead of a constant Doppler shift when they receive the wave train reflected by the other.