February Fourier Talks 2010

John Gray


The Generalized Doppler Effect in Radar with a Discussion of the Mathematics for Representing Functions from a Synesthesia Viewpoint


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 physics-based 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 non-uniform motion upon the received signal at the receiver of the radar. The effect of non-uniform 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 non-uniform Doppler effect.