IEVref:702-04-52ID:
Language:enStatus: Standard
Term: analytic signal
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Definition: complex function whose real part is the real function f(t) representing a signal and whose imaginary part is the Hilbert transform g(t) of the function f(t):

f( t )+jg( t )=f( t ) j π + f( t ) τt dτ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaabAgadaqadaqaaiaadshaaiaawIcacaGLPaaacqGHRaWkcaqGQbGaaeiiaiaabEgadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaqGMbWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaeyOeI0YaaSaaaeaacaqGQbaabaaccaGae8hWdahaamaapedabaWaaSaaaeaacaqGMbWaaeWaaeaacaWG0baacaGLOaGaayzkaaaabaGaeqiXdqNaeyOeI0IaamiDaaaaaSqaaiabgkHiTiabg6HiLcqaaiabgUcaRiabg6HiLcqdcqGHRiI8aOGaaeiiaiaabsgacqaHepaDaaa@580C@

NOTE 1 – The real part f(t) of an analytic signal is the opposite of the Hilbert transform of the imaginary part g(t).

NOTE 2 – If it exists, the complex Fourier transform of an analytic signal is zero for all negative frequencies so that, for instance, the analytic signal can be used to represent a single sideband modulated signal.


Publication date:1992-03
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Internal notes:2017-06-02: Cleanup - Remove Attached Image 702-04-52.gif
2019-08-09: Editorial corrections validated by Erik Jacobson: deletion leading article; correction of presentation of symbols f (6x) AND g (3x); addition of links. JGO
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