An Efficient Method for Calculating the Doppler Spectrum of an Arbitrarily Shaped Object in Uniform Motion

Abstract

In the article, an efficient numerical method for calculating the spectrum of the scattering fields of an arbitrarily shaped object in uniform motion is proposed. This method relies on the frame hopping technique stemming from the special theory of relativity (STR). Firstly, the incident monochromatic plane wave is transformed to the comoving inertial frame in which the object is stationary. Next, the scattering fields of the moving object at the sampling time points are obtained in the comoving frame by solving the electromagnetic (EM) scattering problem with the conventional numerical method in the frequency domain. Then, the spectrum of the scattering fields in the frame in which the observer remains stationary is obtained using the discrete Fourier transform (DFT). The asymptotic expressions for the scattering fields when the moving object is far away from the observation point are derived, by applying which the computation efficiency could be greatly improved.