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Bicoherence: Difference between revisions
→Bicoherence
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The normalization is such that 0 ≤ ''b<sup>2</sup>'' ≤ 1. | The normalization is such that 0 ≤ ''b<sup>2</sup>'' ≤ 1. | ||
The bicoherence is symmetric under the | The bicoherence is symmetric under the transformations ''(ω<sub>1</sub>,ω<sub>2</sub>) → (ω<sub>2</sub>,ω<sub>1</sub>)'' and | ||
''(ω<sub>1</sub>,ω<sub>2</sub>) → (-ω<sub>1</sub>,-ω<sub>2</sub>)'', so that only one quarter of the plane ''(ω<sub>1</sub>,ω<sub>2</sub>)'' contains independent information. | ''(ω<sub>1</sub>,ω<sub>2</sub>) → (-ω<sub>1</sub>,-ω<sub>2</sub>)'', so that only one quarter of the plane ''(ω<sub>1</sub>,ω<sub>2</sub>)'' contains independent information. | ||
Additionally, for discretely sampled data all frequencies must be less than the | Additionally, for discretely sampled data all frequencies must be less than the | ||
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The summed bicoherence is defined by | The summed bicoherence is defined by | ||
:<math>\frac{1}{N} \sum_{\omega_1+\omega_2=\omega}{b^2(\omega_1,\omega_2)} </math> | :<math>\frac{1}{N(\omega)} \sum_{\omega_1+\omega_2=\omega}{b^2(\omega_1,\omega_2)} </math> | ||
where ''N'' is the number of terms in the sum. | where ''N'' is the number of terms in the sum. | ||