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Bicoherence: Difference between revisions
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== Notes == | == Notes == | ||
* The bicoherence can be computed using the (continuous) wavelet transform instead of the Fourier transform, in order to improve statistics. <ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, ''Wavelet bicoherence: a new turbulence analysis tool'', Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | * The bicoherence can be computed using the (continuous) wavelet transform instead of the Fourier transform, in order to improve statistics. <ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, ''Wavelet bicoherence: a new turbulence analysis tool'', Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | ||
* The bicoherence can of course be defined in wavenumber space instead of frequency space by applying the replacements ''t → x'' and ''ω → k''. | |||
* Combined temporal-spatial studies are also possible. <ref>[http://link.aip.org/link/PHPAEN/v17/i5/p052313/s1 T. Yamada, S.-I. Itoh, S. Inagaki, Y. Nagashima, S. Shinohara, N. Kasuya, K. Terasaka, K. Kamataki, H. Arakawa, M. Yagi, A. Fujisawa, and K. Itoh, ''Two-dimensional bispectral analysis of drift wave turbulence in a cylindrical plasma'' , Phys. Plasmas '''17''' (2010) 052313]</ref> | |||
Starting from the spatio-temporal bicorrelation | |||
:<math>C_{22}(x_1,x_2,t_1,t_2) = \left \langle X_1(x,t)X_2(x+x_1,t+t_1)X_2(x+x_2,t+t_2) \right \rangle </math> | |||
the spatio-temporal bispectrum is | |||
:<math>B_2(k_1,k_2,\omega_1,\omega_2) = \hat X_1^*(k,\omega)\hat X_2(k_1,\omega_1) \hat X_2(k_2,\omega_2)</math> | |||
where <math>\omega = \omega_1 + \omega_2</math> and <math>k=k_1+k_2</math>. | |||
== References == | == References == | ||
<references /> | <references /> | ||