We investigate the rotational Doppler effect for the electromagnetic wave carrying orbital angular momentum (OAM) with a method based on spectrum analysis, which is appropriate for both optics and free-space radio cases. We find that the frequency spectrum received is the convolution of emission spectrum and a discrete spectrum about OAM states, and verify it in the numerical simulations as well. This discovery makes it possible to distinguish the linear and rotational Doppler shift, and is helpful to developments of remote sensing and velocimetry in radar.
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