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

Language: | en | Status: backup | |

Term: | analytic signal | ||

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Definition: | a 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):$\text{f}\left(t\right)+\text{jg}\left(t\right)=\text{f}\left(t\right)-\frac{\text{j}}{\pi}{\displaystyle {\int}_{-\infty}^{+\infty}\frac{\text{f}\left(t\right)}{\tau -t}}\text{d}\tau$ NOTE 1 – The real part f( 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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$\text{f}\left(t\right)+\text{jg}\left(t\right)=\text{f}\left(t\right)-\frac{\text{j}}{\pi}{\displaystyle {\int}_{-\infty}^{+\infty}\frac{\text{f}\left(t\right)}{\tau -t}}\text{d}\tau$
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