Title:
The Generalized Doppler Effect in Radar with a Discussion of the Mathematics for Representing Functions from a Synesthesia Viewpoint
Abstract:
The Doppler effect discovery dates back over 150 years. Detailed examination of the effect has a rich history in physics in both the
electromagnetic and acoustical domain, which have led to a number of useful applications in engineering and mathematics. The underlying
explanation for the Doppler effect lies in Relativity (the theory of transformations between moving coordinate frames). A canonical
model for understanding the Doppler effect in radar is the physicsbased model of a moving, perfectly reflecting mirror, which allows
the effect of motion to be analyzed for any radar waveform. The method presented in this presentation allows radar analysis to determine
the functional form of radar return signal due to both uniform and nonuniform motion upon the received signal at the receiver of the
radar. The effect of nonuniform motion for any radar waveform is presented as well as specific examples of nonuniform motion are
discussed. A discussion of how the Doppler effect might be observed from the point of view of a person with synesthesia (a
neurologically based phenomenon in which stimulation of one sensory or cognitive pathway leads to automatic, involuntary experiences in
a second sensory or cognitive pathway). An example of such a radar synesthesia viewpoint is transforming the return radar signal in an
audio form so one can "listen" to a radar waveform, or visualize the signal in the frequency domain by transforming it into a picture.
This suggests a variety of new approaches to representing functions based upon the nonuniform Doppler effect.
