Bicoherence: Difference between revisions

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The normalization is such that 0 &le; ''b<sup>2</sup>'' &le; 1.
The normalization is such that 0 &le; ''b<sup>2</sup>'' &le; 1.


The bicoherence is symmetric under the symmetries ''(&omega;<sub>1</sub>,&omega;<sub>2</sub>) = (&omega;<sub>2</sub>,&omega;<sub>1</sub>)'' and  
The bicoherence is symmetric under the symmetries ''(&omega;<sub>1</sub>,&omega;<sub>2</sub>) &rarr; (&omega;<sub>2</sub>,&omega;<sub>1</sub>)'' and  
''(&omega;<sub>1</sub>,&omega;<sub>2</sub>) = (-&omega;<sub>1</sub>,-&omega;<sub>2</sub>)'', so that only one quarter of the plane ''(&omega;<sub>1</sub>,&omega;<sub>2</sub>)'' contains independent information.
''(&omega;<sub>1</sub>,&omega;<sub>2</sub>) &rarr; (-&omega;<sub>1</sub>,-&omega;<sub>2</sub>)'', so that only one quarter of the plane ''(&omega;<sub>1</sub>,&omega;<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  
Nyquist frequency: ''&omega;<sub>1</sub>,&omega;<sub>2</sub>,&omega; &le; &omega;<sub>Nyq</sub>''. These restrictions define a polygonal subspace of the plane, which is how the bicoherence is usually represented.
Nyquist frequency: ''&omega;<sub>1</sub>,&omega;<sub>2</sub>,&omega; &le; &omega;<sub>Nyq</sub>''. These restrictions define a polygonal subspace of the plane, which is how the bicoherence is usually represented.