Real and complex Doppler effects in lossy media

The theory of the Doppler effect in the presence of lossy media and moving scatterers is investigated. Essentially two kinds of phenomena emerge, which are not distinguishable in the conventional case of lossless media. When the scatterers move uniformly, or the equation of motion involves a slowly varying velocity, it is shown that propagation in lossy media involves complex Doppler effects. The complications introduced by the received complex frequency signal are discussed. It is shown that spectrum broadening occurs, and that, in certain cases, by using judiciously chosen temporal filters, the spectral degradation of the received signal can be counteracted. The second class of phenomena is associated with periodic and harmonic motion, when the scatterer is vibrating around a fixed location. In this case the incident wave is frequency modulated by the moving scatterer, giving rise to sidebands of real frequencies.<>