IEVref: | 702-04-52 | ID: | |

Language: | en | Status: 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):
$f\left(t\right)+\text{j}g\left(t\right)=f\left(t\right)-\frac{\text{j}}{\pi}{\displaystyle {\int}_{-\infty}^{+\infty}\frac{f\left(t\right)}{\tau -t}}\text{d}\tau$ NOTE 1 – The real part 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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$f\left(t\right)+\text{j}g\left(t\right)=f\left(t\right)-\frac{\text{j}}{\pi}{\displaystyle {\int}_{-\infty}^{+\infty}\frac{f\left(t\right)}{\tau -t}}\text{d}\tau$
*t*) of an analytic signal is the opposite of the Hilbert transform of the imaginary part *g*(*t*).