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Bicoherence: Difference between revisions
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(Created page with 'The following applies to the analysis of data or signals :<math>X_i(t)\,</math> The standard cross spectrum is the Fourier transform of the correlation :<math>C_1(t_1) = \left…') |
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:<math>b^2(\omega_1,\omega_2) = \frac{\left \langle |B(\omega_1,\omega_2)|^2 \right \rangle} | :<math>b^2(\omega_1,\omega_2) = \frac{\left \langle |B(\omega_1,\omega_2)|^2 \right \rangle} | ||
{\left \langle |X_1(\omega)|^2\right \rangle\left \langle |X_2(\omega_1) \hat X_2(\omega_2)|^2\right \rangle}</math> | {\left \langle |\hat X_1(\omega)|^2\right \rangle\left \langle | \hat X_2(\omega_1) \hat X_2(\omega_2)|^2\right \rangle}</math> | ||
The normalization is such that 0 ≤ ''b<sup>2</sup>'' ≤ 1. | The normalization is such that 0 ≤ ''b<sup>2</sup>'' ≤ 1. | ||
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:<math>\frac{1}{N_{tot}} \sum_{\omega_1,\omega_2}{b^2(\omega_1,\omega_2)} </math> | :<math>\frac{1}{N_{tot}} \sum_{\omega_1,\omega_2}{b^2(\omega_1,\omega_2)} </math> | ||
where ''N<sub>tot</sub>'' is the number of terms in the sum. | where ''N<sub>tot</sub>'' is the number of terms in the sum. | ||
== Interpretation == | == Interpretation == | ||