Bicoherence: Difference between revisions

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''(&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.
''(&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 (for an example, see [[TJ-II:Turbulence]]).


The summed bicoherence is defined by
The summed bicoherence is defined by