Doppler spectral moments

Statistical moments of Doppler frequency or Doppler velocity, regarding these quantities as continuously distributed random variables with a probability density function equal to the normalized Doppler spectrum.

If S(f) denotes the Doppler spectrum as a function of Doppler frequency f, the nth moment is defined by

where the denominator normalizes the Doppler spectrum to unit area. The nth moment in terms of Doppler velocity is related to that in terms of frequency by

where λ is the radar wavelength. The first moment of velocity is called the mean Doppler velocity and the second central moment is called the Doppler velocity variance. The Doppler spread usually denotes the square root of the Doppler velocity variance.
See Doppler frequency shift.