Doppler spectral moments: Difference between revisions
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Statistical moments of Doppler frequency or [[Doppler velocity]], regarding these quantities as continuously distributed [[random]] variables with a [[probability density function|probability density function]] equal to the normalized [[Doppler spectrum]].<br/> If ''S''(''f'') denotes the Doppler spectrum as a function of Doppler frequency ''f,'' the ''n''th [[moment]] is defined by <blockquote>[[File:ams2001glos-De39.gif|link=|center|ams2001glos-De39]]</blockquote> where the denominator normalizes the Doppler spectrum to unit area. The ''n''th moment in terms of Doppler velocity is related to that in terms of [[frequency]] by <blockquote>[[File:ams2001glos-De40.gif|link=|center|ams2001glos-De40]]</blockquote> where λ is the radar [[wavelength]]. The first [[moment]] of [[velocity]] is called the [[mean Doppler velocity|mean Doppler velocity]] and the second [[central moment]] is called the Doppler velocity [[variance]]. The [[Doppler spread|Doppler spread]] usually denotes the square root of the Doppler velocity variance. <br/>''See'' [[Doppler frequency shift|Doppler frequency shift]]. | |||
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Latest revision as of 13:35, 27 March 2024
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
See Doppler frequency shift.
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.