= h_k^2 A$ and the coupling coefficient as defined above is given by $A_{\bk_0,\bl_0} = A/6$. The factor of one-sixth appears because in the model introduced in this section it is assumed that a coupling occurs at several Fourier components. In the case of only one triad of coupling Fourier components as for the patterns from Section \[secPatternsIntro\], one has $A_{\bk_0,\bl_0} = A$.

The bicoherence of the patterns with nonzero coupling coefficient $A$ is $|b(\bk_0,\bl_0)| = 1$. This is because the signal at Fourier component $\bmm_0$ is entirely due to the nonlinear coupling, and there is no noise or any other independent signal at this component.

The impact of noise on bispectral estimates {#secNoise}
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If noise is present in the data, this reduces the bispectral estimates. If we assume for example that $$\begin{aligned}
X &= X_{\rm G} + X_{\rm NL} + \epsilon \label{eqXnoise},\end{aligned}$$ where $\epsilon(\bx)$ is the noise, which we assume to have independent Gaussian Fourier components and to be independent of $X_{\rm G}$ and $X_{\rm NL}$. If the noise is simply added to the data, the bispectrum (as an expectation value) does not change; see Eqs.  and . However, the estimated coupling coefficient $A_{\bk,\bl}$ and the bicoherence $b$ 