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The theory of the Doppler broadening of radiated or backscattered monochromatic waves is investigated. A simple idealized model is discussed, to show that the classical theory of correlating the frequency spectrum with the line-of-sight velocity-distribution is inadequate. It is demonstrated that relativistic consideration; yield first-order effects which exist even for low velocities. Consequently, if the spectral and velocity-distribution profiles are compared, the spectral curve shows de-emphasis and preemphasis for lower and higher frequencies, respectively. Experimental evidence supports the theory.