Analysis of Dynamic Doppler Effects Using a 4D Frenet-Serret Framework

Highly dynamic motions in physical space create substantial Doppler perturbations in emitted and observed electromagnetic signals.  These perturbations can be characterized in terms of the geometry of the emitter and observer trajectories in 4D spacetime.  I will describe the impact of high speed, acceleration, and jolt on EM signals. I analyze the dynamic Doppler effects using the Frenet-Serret frame of the signal observer and in terms of the curvature, torsion, and hyper-torsion of the observer path in 4D.  Spectral distortions induced by highly maneuverable objects include spectral broadening and nonlinear, asymmetric chirps.  Understanding the spectral effects of dynamic observers is critical for modern wireless communications and radar applications.